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A p p e a r a n c e
F r o m W i k i p e d i a , t h e f r e e e n c y c l o p e d i a
( R e d i r e c t e d f r o m 1 9 9 1 ( n u m b e r ) )
Natural number
Cardinal one thousand Ordinal 1000th Factorization 2 3 3 Divisors 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 Greek numeral ,Α´ Roman numeral M Roman numeral (unicode ) M, m, ↀ Unicode symbol(s )ↀ Greek prefix chilia Latin prefix milli Binary 11111010002 Ternary 11010013 Senary 43446 Octal 17508 Duodecimal 6B412 Hexadecimal 3E816 Tamil ௲ Chinese 千 Punjabi ੧੦੦੦ Devanagari १००० Armenian Ռ Egyptian hieroglyph 𓆼
1000 or one thousand is the natural number following 999 and preceding 1001 . In most English-speaking countries , it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000 .
A group of one thousand things is sometimes known, from Ancient Greek , as a chiliad .[1] Latin , as a millennium . The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand .
Notation [ edit ]
The decimal representation for one thousand is
The SI prefix for a thousand units is "kilo- ", abbreviated to "k"—for instance, a kilogram or "kg" is a thousand grams . This is sometimes extended to non-SI contexts, such as "ka" (kiloannum ) being used as a shorthand for periods of 1000 years. In computer science , however, "kilo-" is used more loosely to mean 2 to the 10th power (1024).
In the SI writing style , a non-breaking space can be used as a thousands separator , i.e., to separate the digits of a number at every power of 1000.
Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the Y2K computer bug of the year 2000.
A thousand units of currency , especially dollars or pounds , are colloquially called a grand . In the United States, this is sometimes abbreviated with a "G" suffix.
Properties [ edit ]
1000 is the 10th icositetragonal number, or 24-gonal number.[2] [3]
1000 is the Wiener index of cycle length 20 labeled boxes arranged as a pyramid with base 1 – 20.[4] [5] [6] [a]
1000 is the element of multiplicity in a
24 ×
24
{\displaystyle 24\times 24}
toroidal board in the n [8] indicator of 25 [9] count of 51 [10] [11]
1000 is the number of strict partitions of 50 subset of the parts .[12]
The regular polygram {1000/499} of the chiliagon , where its diagonals do not pass through the center , yet are closest to it (indistinguishably, unless one zooms in)
A chiliagon polygon ,[13] [14] of order 2000 in its regular form .[b]
Totient values [ edit ]
1000 has a reduced totient value
λ
(
n )
{\displaystyle \lambda (n )}
of 100 ,[20] Euler totient
φ
(
n )
{\displaystyle \varphi (n )}
of 400 .[16]
11 totient value of 1000 (1111, 1255, ..., 3750).[16]
One thousand is also equal to the sum of Euler's totient summatory function
Φ
(
n )
{\displaystyle \Phi (n )}
57 [21]
Repdigits [ edit ]
In decimal , multiples of one thousand are totient values of four-digit repdigits :[16]
In the list of composite numbers , 7777 is very nearly the composite index of 8888: 8886 is the 7779th composite number.[22] [16]
5000 has a totient value of 2000, as does 5050 = 2025 + 3025 = 45 2 55 2
3000 , 5000 and 7000 are the three multiples of one thousand, less than 10 4
10000 4
1600 = 40 2 4 [16] [c]
The sum of the first nine prime numbers up to 23
φ
(
p (
23 )
)
=
1000
{\displaystyle \varphi (p(23 ))=1000}
p (
23 )
=
1255
{\displaystyle p(23 )=1255}
integer partitions of 23.[28]
Prime values [ edit ]
Using decimal representation as well,
997 is the 168th and largest prime number less than 1000 ,[25]
97 100
9 7 10 [22] [25]
On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973 .[25] [d]
1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers:[37]
1,000,999
1,000,999,998,997
1,000,999,998,997,996,995,994,993
all represent prime numbers.[38] [39]
Adding the prime 853 with its prime index of 147[25]
Sporadic groups [ edit ]
The one-thousandth prime number is 7919 1 order of the smallest sporadic group :
|
M
11
|
=
7920
{\displaystyle |\mathrm {M} _{11}|=7920}
[40] [41]
Numbers in the range 1001–1999 [ edit ]
1001 to 1099 [ edit ]
1001 sphenic number (7 × 11 × 13), pentagonal number , pentatope number , palindromic number
1002 = sphenic number, Mertens function zero, abundant number , number of partitions of 22
1003 = the product of some prime p p th p
1004 = heptanacci number [42]
1005 = Mertens function zero, decagonal pyramidal number[43]
1006 = semiprime , product of two distinct isolated primes (2 and 503); unusual number ; square-free number ; number of compositions (ordered partitions ) of 22 into squares; sum of two distinct pentatope numbers (5 and 1001); number of undirected Hamiltonian paths in 4 by 5 square grid graph ;[44] twin primes ;[45] [46] equidigital number ; when turned around, the number looks like a prime, 9001; its cube can be concatenated from other cubes, 1_0_1_8_1_0_8_216 ("_" indicates concatenation, 0 = 03 3 3 3 [47]
1007 = number that is the sum of 8 positive 5th powers[48]
1008 = divisible by the number of primes below it
1009 = smallest four-digit prime , palindromic in bases 11, 15, 19, 24 and 28: (83811 15 19 24 28 Lucky prime and Chen prime .
1010 = 103 [49]
1011 = the largest n n Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction [50]
1012 = ternary number, (32 10 triangular number (triangular number is 253 ),[51] Egyptian fraction [50]
1013 = Sophie Germain prime ,[52] centered square number ,[53]
1014 = 210 [54] [55]
1015 = square pyramidal number [56]
1016 = member of the Mian–Chowla sequence ,[57] stella octangula number , number of surface points on a cube with edge-length 14[58]
1017 = generalized triacontagonal number[59]
1018 = Mertens function zero, 101816 [60]
1019 = Sophie Germain prime ,[52] safe prime ,[61] Chen prime
1020 = polydivisible number
1021 = twin prime with 1019 . It is also a Lucky prime .
1022 = Friedman number
1023 [62] three-dimensional polycubes with 7 [63] elements in a 9-simplex ; highest number one can count to on one's fingers using binary; magic number used in Global Positioning System signals.
1024 2 5 10 bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a Friedman number .
1025 = Proth number 2 10 Moser–de Bruijn sequence , because its base-4 representation (1000014 4 5 0 ); Jacobsthal-Lucas number ; hypotenuse of primitive Pythagorean triangle
1026 = sum of two distinct powers of 2 (1024 + 2
1027 = sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.
1028 = sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9; number of primes <= 213 [64]
1029 = can be written from base 2 to base 18 using only the digits 0 to 9.
1030 = generalized heptagonal number
1031 = exponent and number of ones for the fifth base-10 repunit prime ,[65] Sophie Germain prime ,[52] super-prime , Chen prime
1032 = sum of two distinct powers of 2 (1024 + 8
1033 = emirp , twin prime with 1031
1034 = sum of 12 positive 9th powers[66]
1035 = triangular number ,[67] hexagonal number [68]
1036 = central polygonal number[69]
1037 = number in E-toothpick sequence[70]
1038 = even integer that is an unordered sum of two primes in exactly n [71]
1039 = prime of the form 8n+7,[72] [73] Chen prime
1040 = 45 2 [74]
1041 = sum of 11 positive 5th powers[75]
1042 = sum of 12 positive 5th powers[76]
1043 = number whose sum of even digits and sum of odd digits are even[77]
1044 = sum of distinct powers of 4[74]
1045 = octagonal number [78]
1046 = coefficient of f(q ) (3rd order mock theta function)[79]
1047 = number of ways to split a strict composition of 18 into contiguous subsequences that have the same sum[80]
1048 = number of partitions of 27 into squarefree parts[81]
1049 = Sophie Germain prime ,[52] highly cototient number ,[82] Chen prime
1050 = 10508 to decimal becomes a pronic number (55210 [83] [84]
1051 = centered pentagonal number ,[85] centered decagonal number
1052 = sum of 9 positive 6th powers[86]
1053 = triangular matchstick number[87]
1054 = centered triangular number [88]
1055 = sum of 12 positive 6th powers[89]
1056 = pronic number [90]
1057 = central polygonal number[91]
1058 = sum of 4 positive 5th powers,[92] [93]
1059 = number n 4 [94]
1060 = sum of the first twenty-five primes from 2 97 100 ),[95] 23 131 .[96]
1061 = emirp , twin prime with 1063 , number of prime numbers between 1000 and 10000 (or, number of four-digit primes in decimal representation)[97]
1062 = number that is not the sum of two palindromes [98]
1063 = super-prime , sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime[99]
1064 = sum of two positive cubes [100]
1065 = generalized duodecagonal[101]
1066 = number whose sum of their divisors is a square [102]
1067 = number of strict integer partitions of 45 in which are empty or have smallest part not dividing the other ones[103]
1068 = number that is the sum of 7 positive 5th powers,[46] [104]
1069 = emirp [105]
1070 = number that is the sum of 9 positive 5th powers[106]
1071 = heptagonal number [107]
1072 = centered heptagonal number [108]
1073 = number that is the sum of 12 positive 5th powers[76]
1074 = number that is not the sum of two palindromes [98]
1075 = number non-sum of two palindromes [98]
1076 = number of strict trees weight 11[109]
1077 = number where 7 [110]
1078 = Euler transform of negative integers [111]
1079 = every positive integer is the sum of at most 1079 tenth powers.
1080 = pentagonal number[112]
1081 = triangular number,[67] Padovan sequence [113]
1082 = central polygonal number[69]
1083 = three-quarter square ,[114] [115]
1084 = third spoke of a hexagonal spiral,[116] 108464
1085 = number of partitions of n parts > or = 2 [117]
1086 = Smith number ,[118]
1087 = super-prime, cousin prime , lucky prime [119]
1088 = octo-triangular number , (triangular number result being 136 )[120] 1024 + 64 [121] primes with the inclusion of multiplicity [122]
1089 2 nonagonal number , centered octagonal number , first natural number whose digits in its decimal representation get reversed when multiplied by 9.[123]
1090 = sum of 5 positive 5th powers[124]
1091 = cousin prime and twin prime with 1093
1092 = divisible by the number of primes below it
1093 Wieferich prime (the only other known Wieferich prime is 3511[125] twin prime with 1091 and star number [126]
1094 = sum of 9 positive 5th powers,[106] 109464
1095 = sum of 10 positive 5th powers,[127] palindromes
1096 = hendecagonal number,[128] [129]
1097 = emirp ,[105] Chen prime
1098 = multiple of 9 containing digit 9 in its base-10 representation[130]
1099 = number where 9 outnumbers every other digit[131]
1100 to 1199 [ edit ]
1100 = number of partitions of 61 into distinct squarefree parts[132]
1101 = pinwheel number[133]
1102 = sum of totient function for first 60 integers
1103 = Sophie Germain prime ,[52] balanced prime [134]
1104 = Keith number [135]
1105 2 2 2 2 2 2 2 2 Carmichael number ,[136] magic constant of n n magic square and n n decagonal number ,[137] [53] Fermat pseudoprime [138]
1106 = number of regions into which the plane is divided when drawing 24 ellipses[139]
1107 = number of non-isomorphic strict T0 multiset partitions of weight 8[140]
1108 = number k such that k64
1109 = Friedlander-Iwaniec prime,[141] Chen prime
1110 = k such that 2k [142]
1111 = 11 × 101, palindrome that is a product of two palindromic primes,[143] repunit [144]
1112 = k such that 9k [145]
1113 = number of strict partions of 40[146]
1114 = number of ways to write 22 as an orderless product of orderless sums[147]
1115 = number of partitions of 27 into a prime number of parts[148]
1116 = divisible by the number of primes below it
1117 = number of diagonally symmetric polyominoes with 16 cells,[149] Chen prime
1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}[150]
1119 = number of bipartite graphs with 9 nodes[151]
1120 = number k such that k64
1121 = number of squares between 342 4 [152]
1122 = pronic number,[90]
1123 = balanced prime [134]
1124 = Leyland number [153] 10 2
1125 = Achilles number
1126 = number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}[154]
1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts[155]
1128 = 47th triangular number,[67] [68] 188 × 6 [156] vertex operator algebra with central charge of 24, D 24 [157]
1129 = number of lattice points inside a circle of radius 19[158]
1130 = skiponacci number[159]
1131 = number of edges in the hexagonal triangle T(26 )[160]
1132 = number of simple unlabeled graphs with 9 nodes of 2 colors whose components are complete graphs[161]
1133 = number of primitive subsequences of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}[162]
1134 = divisible by the number of primes below it, triangular matchstick number[87]
1135 = centered triangular number [163]
1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph [164]
1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid[165]
1138 = recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138 Star Wars
1139 = wiener index of the windmill graph D(3,17)[166]
1140 = tetrahedral number [167]
1141 = 7-Knödel number[168]
1142 = n such that n32 [169]
1143 = number of set partitions of 8 elements with 2 connectors[170]
1144 is not the sum of a pair of twin primes[171]
1145 = 5-Knödel number [172]
1146 is not the sum of a pair of twin primes[171]
1147 = 31 × 37 (a product of 2 successive primes)[173]
1148 is not the sum of a pair of twin primes[171]
1149 = a product of two palindromic primes[174]
1150 = number of 11-iamonds without bilateral symmetry.[175]
1151 = first prime following a prime gap of 22,[176] Chen prime
1152 = highly totient number ,[177] 3-smooth number (2 7 2 [93] Achilles number
1153 = super-prime , Proth prime [178]
1154 = 2 × 242 [179]
1155 = number of edges in the join of two cycle graphs, both of order 33[180]
1156 = 342 octahedral number ,[181] [85] [182]
1157 = smallest number that can be written as n^2+1 without any prime factors that can be written as a^2+1.[183]
1158 = number of points on surface of octahedron with edgelength 17[184]
1159 = member of the Mian–Chowla sequence,[57] a centered octahedral number [185]
1160 = octagonal number [186]
1161 = sum of the first twenty-six primes
1162 = pentagonal number,[112]
1163 = smallest prime >34 2 [187] Legendre's conjecture . Chen prime .
1164 = number of chains of multisets that partition a normal multiset of weight 8, where a multiset is normal if it spans an initial interval of positive integers[188]
1165 = 5-Knödel number [172]
1166 = heptagonal pyramidal number[189]
1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43[190]
1168 = antisigma(49 )[191]
1169 = highly cototient number[82]
1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match
1171 = super-prime
1172 = number of subsets of first 14 integers that have a sum divisible by 14[192]
1173 = number of simple triangulation on a plane with 9 nodes[193]
1174 = number of widely totally strongly normal compositions of 16
1175 = maximal number of pieces that can be obtained by cutting an annulus with 47 cuts[155]
1176 = triangular number[67]
1177 = heptagonal number[107]
1178 = number of surface points on a cube with edge-length 15[58]
1179 = number of different permanents of binary 7*7 matrices[194]
1180 = smallest number of non-integral partitions into non-integral power >1000.[195]
1181 = smallest k over 1000 such that 8*10^k-49 is prime.[196]
1182 = number of necklaces possible with 14 beads of 2 colors (that cannot be turned over)[197]
1183 = pentagonal pyramidal number
1184 = amicable number with 1210[198]
1185 = number of partitions of 45 into pairwise relatively prime parts[199]
1186 = number of diagonally symmetric polyominoes with 15 cells,[149] number of partitions of 54 into prime parts
1187 = safe prime,[61] Stern prime ,[200] [134] Chen prime
1188 = first 4 digit multiple of 18 to contain 18[201]
1189 = number of squares between 352 4 [152]
1190 = pronic number,[90] [202]
1191 = 352 35 [203]
1192 = sum of totient function for first 62 integers
1193 = a number such that 4 1193 - 31193 is primeChen prime
1194 =number of permutations that can be reached with 8 moves of 2 bishops and 1 rook on a 3 × 3 chessboard[204]
1195 = smallest four digit number for which a−1 (n ) is an integer is a(n ) is 2*a(n-1) - (-1)n [205]
1196 =
∑
k =
1
38
σ
(
k )
{\displaystyle \sum _{k=1}^{38}\sigma (k )}
[206]
1197 = pinwheel number[133]
1198 = centered heptagonal number[108]
1199 = area of the 20th conjoined trapezoid [207]
1200 to 1299 [ edit ]
1200 = the long thousand long hundreds " of 120 each, the traditional reckoning of large numbers in Germanic languages , the number of households the Nielsen ratings sample,[208] number k such that k64
1201 = centered square number,[53] super-prime , centered decagonal number
1202 = number of regions the plane is divided into by 25 ellipses[139]
1203 : first 4 digit number in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane[209]
1204 : magic constant of a 7 × 7 × 7 magic cube[210]
1205 = number of partitions of 28 such that the number of odd parts is a part[211]
1206 = 29-gonal number [212]
1207 = composite de Polignac number [213]
1208 = number of strict chains of divisors starting with the superprimorial A006939(3 )[214]
1209 = The product of all ordered non-empty subsets of {3,1} if {a,b} is a||b: 1209=1*3*13*31
1210 = amicable number with 1184[215]
1211 = composite de Polignac number [213]
1212 =
∑
k =
0
17
p (
k )
{\displaystyle \sum _{k=0}^{17}p(k )}
p
{\displaystyle p}
k
{\displaystyle k}
[216]
1213 = emirp
1214 = sum of first 39 composite numbers,[217]
1215 = number of edges in the hexagonal triangle T(27 )[160]
1216 = nonagonal number[218]
1217 = super-prime , Proth prime[178]
1218 = triangular matchstick number[87]
1219 = Mertens function zero, centered triangular number [163]
1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons[219]
1221 = product of the first two digit, and three digit repdigit
1222 = hexagonal pyramidal number
1223 = Sophie Germain prime ,[52] [134]
1224 = number of edges in the join of two cycle graphs, both of order 34[180]
1225 = 352 square triangular number ,[220] [68] [221] [222] [223]
1226 = number of rooted identity trees with 15 nodes [224]
1227 = smallest number representable as the sum of 3 triangular numbers in 27 ways[225]
1228 = sum of totient function for first 63 integers
1229 = Sophie Germain prime ,[52] emirp
1230 = the Mahonian number: T(9, 6)[226]
1231 = smallest mountain emirp, as 121, smallest mountain number is 11 × 11
1232 = number of labeled ordered set of partitions of a 7-set into odd parts[227]
1233 = 122 2
1234 [84]
1235 = excluding duplicates, contains the first four Fibonacci numbers [228]
1236 = 617 + 619: sum of twin prime pair[229]
1237 = prime of the form 2p-1
1238 = number of partitions of 31 that do not contain 1 as a part[73]
1239 = toothpick number in 3D[230]
1240 = square pyramidal number[56]
1241 = centered cube number ,[231]
1242 = decagonal number[137]
1243 = composite de Polignac number [213]
1244 = number of complete partitions of 25[232]
1245 = Number of labeled spanning intersecting set-systems on 5 vertices.[233]
1246 = number of partitions of 38 such that no part occurs more than once[234]
1247 = pentagonal number[112]
1248 = the first four powers of 2 concatenated together
1249 = emirp, trimorphic number [235]
1250 = area of a square with diagonal 50[93]
1251 = 2 × 252 [236]
1252 = 2 × 252 [179]
1253 = number of partitions of 23 with at least one distinct part[237]
1254 = number of partitions of 23 into relatively prime parts[238]
1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,[147] [239]
1256 = 1 × 2 × (5 2 2 [240]
1257 = number of lattice points inside a circle of radius 20[158]
1258 = 1 × 2 × (5 2 2 [240]
1259 = highly cototient number [82]
1260 = highly composite number ,[241] [90] vampire number ,[242] [146] Book of Revelation
1261 = star number,[126]
1262 = maximal number of regions the plane is divided into by drawing 36 circles[243]
1263 = rounded total surface area of a regular tetrahedron with edge length 27[244]
1264 = sum of the first 27 primes
1265 = number of rooted trees with 43 vertices in which vertices at the same level have the same degree[245]
1266 = centered pentagonal number,[85]
1267 = 7-Knödel number[168]
1268 = number of partitions of 37 into prime power parts[246]
1269 = least number of triangles of the Spiral of Theodorus to complete 11 revolutions[247]
1270 = 25 + 24×26 + 23×27,[248]
1271 = sum of first 40 composite numbers[217]
1272 = sum of first 41 nonprimes[249]
1273 = 19 × 67 = 19 × prime(19 )[250]
1274 = sum of the nontriangular numbers between successive triangular numbers
1275 = triangular number,[67]
1276 = number of irredundant sets in the 25-cocktail party graph[251]
1277 = the start of a prime constellation of length 9 (a "prime nonuple")
1278 = number of Narayana's cows and calves after 20 years[252]
1279 = Mertens function zero, Mersenne prime exponent
1280 = Mertens function zero, number of parts in all compositions of 9[253]
1281 = octagonal number [186]
1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts[199]
1283 = safe prime[61]
1284 = 641 + 643: sum of twin prime pair[229]
1285 = Mertens function zero, number of free nonominoes , number of parallelogram polyominoes with 10 cells.[254]
1286 = number of inequivalent connected planar figures that can be formed from five 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree[255]
1287 =
(
13 5
)
{\displaystyle {13 \choose 5}}
[256]
1288 = heptagonal number[107]
1289 [52]
1290 =
1289
+
1291
2
{\displaystyle {\frac {1289+1291}{2}}}
[257]
1291 = largest prime <6 4 [258]
1292 = number such that phi(1292) = phi(sigma(1292)),[259]
1293 =
∑
j =
1
n
j ×
p r i m e (
j )
{\displaystyle \sum _{j=1}^{n}j\times prime(j )}
[260]
1294 = rounded volume of a regular octahedron with edge length 14[261]
1295 = number of edges in the join of two cycle graphs, both of order 35[180]
1296 = 362 4 rectangles on a normal 8 × 8 chessboard , also the maximum font size allowed in Adobe InDesign, number of combinations of 2 characters(00-ZZ)
1297 = super-prime , Mertens function zero, pinwheel number[133]
1298 = number of partitions of 55 into prime parts
1299 = Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts[262]
1300 to 1399 [ edit ]
1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match; smallest even odd-factor hyperperfect number
1301 = centered square number,[53] [263] [264]
1302 = Mertens function zero, number of edges in the hexagonal triangle T(28 )[160]
1303 = prime of form 21n+1 and 31n+1[265] [266]
1304 = sum of 13046 9
1305 = triangular matchstick number[87]
1306 = Mertens function zero. In base 10 , raising the digits of 1306 to powers of successive integers equals itself: 1306 = 11 2 3 4 135 , 175 , 518 , and 598 also have this property. Centered triangular number .[163]
1307 = safe prime[61]
1308 = sum of totient function for first 65 integers
1309 = the first sphenic number followed by two consecutive such number
1310 = smallest number in the middle of a set of three sphenic numbers
1311 = number of integer partitions of 32 with no part dividing all the others[267]
1312 = member of the Mian-Chowla sequence;[57]
1313 = sum of all parts of all partitions of 14 [268]
1314 = number of integer partitions of 41 whose distinct parts are connected[269]
1315 = 10^(2n+1)-7*10^n-1 is prime.[270]
1316 = Euler transformation of sigma(11 )[271]
1317 = 1317 Only odd four digit number to divide the concatenation of all number up to itself in base 25[272]
1318 512 + 1 is prime,[273]
1319 = safe prime[61]
1320 = 659 + 661: sum of twin prime pair[229]
1321 = Friedlander-Iwaniec prime[141]
1322 = area of the 21st conjoined trapezoid [207]
1323 = Achilles number
1324 = if D(n ) is the nth representation of 1, 2 arranged lexicographically. 1324 is the first non-1 number which is D(D(x ))[274]
1325 = Markov number ,[275] [276]
1326 = triangular number,[67] [68]
1327 = first prime followed by 33 consecutive composite numbers
1328 = sum of totient function for first 66 integers
1329 = Mertens function zero, sum of first 41 composite numbers[217]
1330 = tetrahedral number,[153] Ruth–Aaron pair with 1331 under second definition
1331 = 113 [108] x 2 x x
1332 = pronic number[90]
1333 = 372 37 [203]
1334 = maximal number of regions the plane is divided into by drawing 37 circles[243]
1335 = pentagonal number,[112]
1336 = sum of gcd(x, y) for 1 <= x, y <= 24,[277]
1337 = Used in the novel form of spelling called leet . Approximate melting point of gold in kelvins .
1338 = atomic number of the noble element of period 18,[278]
1339 = First 4 digit number to appear twice in the sequence of sum of cubes of primes dividing n[279]
1340 = k such that 5 × 2k [280]
1341 = First mountain number with 2 jumps of more than one.
1342 =
∑
k =
1
40
σ
(
k )
{\displaystyle \sum _{k=1}^{40}\sigma (k )}
[206]
1343 = cropped hexagone [281]
1344 = 372 2 [282]
1345 = k such that k, k+1 and k+2 are products of two primes[283]
1346 = number of locally disjointed rooted trees with 10 nodes[284]
1347 = concatenation of first 4 Lucas numbers [285]
1348 = number of ways to stack 22 pennies such that every penny is in a stack of one or two[286]
1349 = Stern-Jacobsthal number[287]
1350 = nonagonal number[218]
1351 = number of partitions of 28 into a prime number of parts[148]
1352 = number of surface points on a cube with edge-length 16,[58] Achilles number
1353 = 2 × 262 [236]
1354 = 2 × 262 [179]
1355 appears for the first time in the Recamán's sequence at n = 325,374,625,245.[288] [289] [290]
1356 is not the sum of a pair of twin primes[171]
1357 = number of nonnegative solutions to x2 2 2 [291]
1358 = rounded total surface area of a regular tetrahedron with edge length 28[244]
1359 is the 42d term of Flavius Josephus's sieve[292]
1360 = 372 2 [282]
1361 = first prime following a prime gap of 34,[176] centered decagonal number , 3rd Mills' prime , Honaker prime[263]
1362 = number of achiral integer partitions of 48[293]
1363 = the number of ways to modify a circular arrangement of 14 objects by swapping one or more adjacent pairs[294]
1364 = Lucas number[295]
1365 = pentatope number[296]
1366 = Arima number, after Yoriyuki Arima who in 1769 constructed this sequence as the number of moves of the outer ring in the optimal solution for the Chinese Rings puzzle[297]
1367 = safe prime,[61] [134]
1368 = number of edges in the join of two cycle graphs, both of order 36[180]
1369 = 372 [221]
1370 = σ2 37 ): sum of squares of divisors of 37[298]
1371 = sum of the first 28 primes
1372 = Achilles number
1373 = number of lattice points inside a circle of radius 21[158]
1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}[150]
1375 = decagonal pyramidal number[299]
1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers )[300]
1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts[155]
1378 = triangular number[67]
1379 = magic constant of n n magic square and n n
1380 = number of 8-step mappings with 4 inputs[301]
1381 = centered pentagonal number[85]
1382 = first 4 digit tetrachi number [302]
1383 = 3 × 461. 101383 + 7 is prime[303]
1384 =
∑
k =
1
41
σ
(
k )
{\displaystyle \sum _{k=1}^{41}\sigma (k )}
[206]
1385 = up/down number[304]
1386 = octagonal pyramidal number[305]
1387 = 5th Fermat pseudoprime of base 2,[306] centered hexagonal number and the 19th decagonal number ,[137] Super-Poulet number .[307]
1388 = 4 × 192 Ulams spiral [308]
1389 = sum of first 42 composite numbers[217]
1390 = sum of first 43 nonprimes[249]
1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47[190]
1392 = number of edges in the hexagonal triangle T(29 )[160]
1393 = 7-Knödel number[168]
1394 = sum of totient function for first 67 integers
1395 = vampire number ,[242] [57] [87]
1396 = centered triangular number [163]
1397 =
⌊
5
9 2
⌋
{\displaystyle \left\lfloor 5^{\frac {9}{2}}\right\rfloor }
[309]
1398 = number of integer partitions of 40 whose distinct parts are connected[269]
1399 = emirp[310]
1400 to 1499 [ edit ]
1400 = number of sum-free subsets of {1, ..., 15}[311]
1401 = pinwheel number[133]
1402 = number of integer partitions of 48 whose augmented differences are distinct,[312] [313]
1403 = smallest x such that M(x ) = 11, where M() is Mertens function [314]
1404 = heptagonal number[107]
1405 = 262 2 2 2 2 [53]
1406 = pronic number,[90] semi-meandric number [315]
1407 = 382 38 [203]
1408 = maximal number of regions the plane is divided into by drawing 38 circles[243]
1409 = super-prime , Sophie Germain prime,[52] [178]
1410 = denominator of the 46th Bernoulli number [316]
1411 = LS(41 )[317]
1412 = LS(42 ),[317]
1413 = LS(43 )[317]
1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations[318]
1415 = the Mahonian number: T(8, 8)[226]
1416 = LS(46 )[317]
1417 = number of partitions of 32 in which the number of parts divides 32[319]
1418 = smallest x such that M(x ) = 13, where M() is Mertens function [314]
1419 = Zeisel number [320]
1420 = Number of partitions of 56 into prime parts
1421 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 29-manifold to be realizable as a sub-manifold,[321]
1422 = number of partitions of 15 with two parts marked[322]
1423 = 200 + 1223 and the 200th prime is 1223[323]
1424 = number of nonnegative solutions to x2 2 2 [291]
1425 = self-descriptive number in base 5
1426 = sum of totient function for first 68 integers, pentagonal number,[112] [146]
1427 = twin prime together with 1429[324]
1428 = number of complete ternary trees with 6 internal nodes, or 18 edges[325]
1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts[262]
1430 = Catalan number [326]
1431 = triangular number,[67] [68]
1432 = member of Padovan sequence[113]
1433 = super-prime , Honaker prime,[263] Microsoft SQL Server databases
1434 = rounded volume of a regular tetrahedron with edge length 23[327]
1435 = vampire number ;[242] 8 + 1 2 m )
1436 = discriminant of a totally real cubic field[328]
1437 = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^[329]
1438 = k such that 5 × 2k [280]
1439 = Sophie Germain prime,[52] [61]
1440 = a highly totient number [177] gonal number . Also, the number of minutes in one day, the blocksize of a standard 3 + 1 / 2 floppy disk , and the horizontal resolution of WXGA(II ) computer displays
1441 = star number[126]
1442 = number of parts in all partitions of 31 into distinct parts[84]
1443 = the sum of the second trio of three-digit permutable primes in decimal : 337 , 373 , and 733 . Also the number of edges in the join of two cycle graphs, both of order 37 [180]
1444 = 382 pandigital number in Roman numerals
1445 =
∑
k =
0
3
(
(
3 k
)
×
(
3 +
k
k
)
)
2
{\displaystyle \sum _{k=0}^{3}\left({\binom {3}{k}}\times {\binom {3+k}{k}}\right)^{2}}
[330]
1446 = number of points on surface of octahedron with edgelength 19[184]
1447 = super-prime , happy number
1448 = number k such that phi(prime(k )) is a square[331]
1449 = Stella octangula number
1450 = σ2 34 ): sum of squares of divisors of 34[298]
1451 = Sophie Germain prime[52]
1452 = first Zagreb index of the complete graph K12 [332]
1453 = Sexy prime with 1459
1454 = 3 × 222 [333]
1455 = k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1456 = number of regions in regular 15-gon with all diagonals drawn[335]
1457 = 2 × 272 twin square [336]
1458 maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×36
1459 = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), pierpont prime
1460 = The number of years that would have to pass in the Julian calendar in order to accrue a full year's worth of leap days.
1461 = number of partitions of 38 into prime power parts[246]
1462 = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices[337]
1463 = total number of parts in all partitions of 16[104]
1464 = rounded total surface area of a regular icosahedron with edge length 13[338]
1465 = 5-Knödel number [172]
1466 =
∑
k =
1
256
d (
k )
{\displaystyle \sum _{k=1}^{256}d(k )}
d (
k )
{\displaystyle d(k )}
k
{\displaystyle k}
[339]
1467 = number of partitions of 39 with zero crank[340]
1468 = number of polyhexes with 11 cells that tile the plane by translation[341]
1469 = octahedral number,[181] [82]
1470 = pentagonal pyramidal number ,[342]
1471 = super-prime , centered heptagonal number[108]
1472 = number of overpartitions of 15[343]
1473 = cropped hexagone [281]
1474 =
44 (
44 +
1 )
2
+
44
2
4
{\displaystyle {\frac {44(44+1)}{2}}+{\frac {44^{2}}{4}}}
44 ) + A002620(44 ))[344]
1475 = number of partitions of 33 into parts each of which is used a different number of times[345]
1476 = coreful perfect number[346]
1477 = 7-Knödel number[168]
1478 = total number of largest parts in all compositions of 11[347]
1479 = number of planar partitions of 12[348]
1480 = sum of the first 29 primes
1481 = Sophie Germain prime[52]
1482 = pronic number,[90] [349]
1483 = 392 39 [203]
1484 = maximal number of regions the plane is divided into by drawing 39 circles[243]
1485 = triangular number
1486 = number of strict solid partitions of 19[129]
1487 = safe prime[61]
1488 = triangular matchstick number[87]
1489 = centered triangular number [163]
1490 = tetranacci number [350]
1491 = nonagonal number,[218]
1492 = discriminant of a totally real cubic field,[328]
1493 = Stern prime[200]
1494 = sum of totient function for first 70 integers
1495 = 9###[351]
1496 = square pyramidal number[56]
1497 = skiponacci number[159]
1498 = number of flat partitions of 41[352]
1499 = Sophie Germain prime,[52] super-prime
1500 to 1599 [ edit ]
1500 = hypotenuse in three different Pythagorean triangles[353]
1501 = centered pentagonal number[85]
1502 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47[354]
1503 = least number of triangles of the Spiral of Theodorus to complete 12 revolutions[247]
1504 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers )[300]
1505 = number of integer partitions of 41 with distinct differences between successive parts[355]
1506 = number of Golomb partitions of 28[356]
1507 = number of partitions of 32 that do not contain 1 as a part[73]
1508 = heptagonal pyramidal number[189]
1509 = pinwheel number[133]
1510 deficient number , odious number
1511 = Sophie Germain prime,[52] [134]
1512 = k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1513 = centered square number[53]
1514 = sum of first 44 composite numbers[217]
1515 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 30-manifold to be realizable as a sub-manifold[321]
1516 =
⌊
9
10 3
⌋
{\displaystyle \left\lfloor 9^{\frac {10}{3}}\right\rfloor }
[357]
1517 = number of lattice points inside a circle of radius 22[158]
1518 = sum of first 32 semiprimes,[358]
1519 = number of polyhexes with 8 cells,[359]
1520 = pentagonal number,[112]
1521 = 392 [221]
1522 = k such that 5 × 2k [280]
1523 = super-prime , Mertens function zero, safe prime,[61] [57]
1524 = Mertens function zero, k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1525 = heptagonal number,[107]
1526 = number of conjugacy classes in the alternating group A27 [360]
1527 = number of 2-dimensional partitions of 11,[361]
1528 = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21[362]
1529 = composite de Polignac number [213]
1530 = vampire number [242]
1531 = prime number, centered decagonal number , Mertens function zero
1532 = number of series-parallel networks with 9 unlabeled edges,[363]
1533 = 21 × 73 = 21 × 21st prime[250]
1534 = number of achiral integer partitions of 50[293]
1535 = Thabit number
1536 = a common size of microplate , 3-smooth number (2 9 [364]
1537 = Keith number,[135]
1538 = number of surface points on a cube with edge-length 17[58]
1539 = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts[155]
1540 = triangular number, hexagonal number,[68] [137] [153]
1541 = octagonal number [186]
1542 = k such that 2^k starts with k[365]
1543 = prime dividing all Fibonacci sequences,[366]
1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length[367]
1545 = number of reversible string structures with 9 beads using exactly three different colors[368]
1546 = number of 5 X 5 binary matrices with at most one 1 in each row and column,[369]
1547 = hexagonal pyramidal number
1548 = coreful perfect number[346]
1549 = de Polignac prime[370]
1550 =
31 ×
(
3 ×
31 +
7 )
2
{\displaystyle {\frac {31\times (3\times 31+7)}{2}}}
[371]
1551 = 6920 - 5369 = A169952(24 ) - A169952(23 ) = A169942(24 ) = number of Golomb rulers of length 24[372] [373]
1552 = Number of partitions of 57 into prime parts
1553 = 509 + 521 + 523 = a prime that is the sum of three consecutive primes[374]
1554 = 2 × 3 × 7 × 37 = product of four distinct primes[375]
1555 2 1554 [376]
1556 = sum of the squares of the first nine primes
1557 = number of graphs with 8 nodes and 13 edges[377]
1558 = number k such that k64
1559 = Sophie Germain prime[52]
1560 = pronic number[90]
1561 = a centered octahedral number ,[185] [378]
1562 = maximal number of regions the plane is divided into by drawing 40 circles[243]
1563 =
∑
k =
1
50
50
gcd
(
50 ,
k )
{\displaystyle \sum _{k=1}^{50}{\frac {50}{\gcd(50,k)}}}
[379]
1564 = sum of totient function for first 71 integers
1565 =
1036
2
+
1173
2
{\displaystyle {\sqrt {1036^{2}+1173^{2}}}}
1036
+
1173
=
47
2
{\displaystyle 1036+1173=47^{2}}
[380]
1566 = number k such that k64
1567 = number of partitions of 24 with at least one distinct part[237]
1568 = Achilles number [381]
1569 = 2 × 282 [236]
1570 = 2 × 282 [179]
1571 = Honaker prime[263]
1572 = member of the Mian–Chowla sequence[57]
1573 = discriminant of a totally real cubic field[328]
1574 256 + 1 is prime[382]
1575 = odd abundant number ,[383] sum of the nontriangular numbers between successive triangular numbers , number of partitions of 24[239]
1576 14 [384]
1577 = sum of the quadratic residues of 83[385]
1578 = sum of first 45 composite numbers[217]
1579 = number of partitions of 54 such that the smallest part is greater than or equal to number of parts[262]
1580 = number of achiral integer partitions of 51[293]
1581 = number of edges in the hexagonal triangle T(31 )[160]
1582 = a number such that the integer triangle [A070080(1582), A070081(1582), A070082(1582)] has an integer area[386]
1583 = Sophie Germain prime
1584 = triangular matchstick number[87]
1585 = Riordan number , centered triangular number [163]
1586 = area of the 23rd conjoined trapezoid [207]
1587 = 3 × 232 23,23,23 [387]
1588 = sum of totient function for first 72 integers
1589 = composite de Polignac number [213]
1590 = rounded volume of a regular icosahedron with edge length 9[388]
1591 = rounded volume of a regular octahedron with edge length 15[261]
1592 = sum of all divisors of the first 36 odd numbers[389]
1593 = sum of the first 30 primes
1594 = minimal cost of maximum height Huffman tree of size 17[390]
1595 = number of non-isomorphic set-systems of weight 10
1596 = triangular number
1597 = Fibonacci prime ,[391] Markov prime ,[275] super-prime , emirp
1598 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}[150]
1599 = number of edges in the join of two cycle graphs, both of order 39[180]
1600 to 1699 [ edit ]
1600 = 402 [392] 7 White House , length in meters of a common High School Track Event, perfect score on SAT (except from 2005 to 2015)
1601 = Sophie Germain prime, Proth prime,[178] 1601 (Mark Twain)
1602 = number of points on surface of octahedron with edgelength 20[184]
1603 = number of partitions of 27 with nonnegative rank[393]
1604 = number of compositions of 22 into prime parts[394]
1605 = number of polyominoes consisting of 7 regular octagons[395]
1606 = enneagonal pyramidal number[396]
1607 = member of prime triple with 1609 and 1613[397]
1608 =
∑
k =
1
44
σ
(
k )
{\displaystyle \sum _{k=1}^{44}\sigma (k )}
[206]
1609 = cropped hexagonal number [281]
1610 = number of strict partions of 43[146]
1611 = number of rational numbers which can be constructed from the set of integers between 1 and 51[190]
1612 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 31-manifold to be realizable as a sub-manifold[321]
1613 , 1607 and 1619 are all primes[398]
1614 = number of ways of refining the partition 8^1 to get 1^8[399]
1615 = composite number such that the square mean of its prime factors is a nonprime integer[400]
1616 =
16 (
16
2
+
3 ×
16 −
1 )
3
{\displaystyle {\frac {16(16^{2}+3\times 16-1)}{3}}}
3 [401]
1617 = pentagonal number[112]
1618 = centered heptagonal number[108]
1619 = palindromic prime in binary , safe prime[61]
1620 = 809 + 811: sum of twin prime pair[229]
1621 = super-prime , pinwheel number[133]
1622 = semiprime of the form prime + 1[402]
1623 is not the sum of two triangular numbers and a fourth power[403]
1624 = number of squares in the Aztec diamond of order 28[404]
1625 = centered square number[53]
1626 = centered pentagonal number[85]
1627 = prime and 2 × 1627 - 1 = 3253 is also prime[405]
1628 = centered pentagonal number[85]
1629 = rounded volume of a regular tetrahedron with edge length 24[327]
1630 = number k such that k^64 + 1 is prime
1631 =
∑
k =
0
5
(
k +
1 )
!
(
5 k
)
{\displaystyle \sum _{k=0}^{5}(k+1)!{\binom {5}{k}}}
[406]
1632 = number of acute triangles made from the vertices of a regular 18-polygon[407]
1633 = star number[126]
1634 = Narcissistic number in base 10
1635 = number of partitions of 56 whose reciprocal sum is an integer[408]
1636 = number of nonnegative solutions to x2 2 2 [291]
1637 = prime island: least prime whose adjacent primes are exactly 30 apart[409]
1638 = harmonic divisor number ,[410] 1638 - 1 is prime[280]
1639 = nonagonal number[218]
1640 = pronic number[90]
1641 = 412 41 [203]
1642 = maximal number of regions the plane is divided into by drawing 41 circles[243]
1643 = sum of first 46 composite numbers[217]
1644 = 821 + 823: sum of twin prime pair[229]
1645 = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection[411]
1646 = number of graphs with 8 nodes and 14 edges[377]
1647 and 1648 are both divisible by cubes[412]
1648 = number of partitions of 343 [413]
1649 = highly cototient number,[82] [153]
1650 = number of cards to build an 33-tier house of cards[202]
1651 = heptagonal number[107]
1652 = number of partitions of 29 into a prime number of parts[148]
1653 = triangular number, hexagonal number,[68] [158]
1654 = number of partitions of 42 into divisors of 42[414]
1655 = rounded volume of a regular dodecahedron with edge length 6[415]
1656 = 827 + 829: sum of twin prime pair[229]
1657 = cuban prime ,[416]
1658 = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations[318]
1659 = number of rational numbers which can be constructed from the set of integers between 1 and 52[190]
1660 = sum of totient function for first 73 integers
1661 = 11 × 151, palindrome that is a product of two palindromic primes[143]
1662 = number of partitions of 49 into pairwise relatively prime parts[199]
1663 = a prime number and 51663 - 41663 is a 1163-digit prime number[417]
1664 = k such that k, k+1 and k+2 are sums of 2 squares[418]
1665 = centered tetrahedral number[276]
1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)
1667 = 228 + 1439 and the 228th prime is 1439[323]
1668 = number of partitions of 33 into parts all relatively prime to 33[419]
1669 = super-prime , smallest prime with a gap of exactly 24 to the next prime[420]
1670 = number of compositions of 12 such that at least two adjacent parts are equal[421]
1671 divides the sum of the first 1671 composite numbers[422]
1672 = 412 2 [282]
1673 = RMS number[423]
1674 = k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1675 = Kin number[424]
1676 = number of partitions of 34 into parts each of which is used a different number of times[345]
1677 = 412 2 [282]
1678 = n such that n32 [169]
1679 = highly cototient number,[82] Arecibo message ), number of parts in all partitions of 32 into distinct parts[84]
1680 = highly composite number,[241] [180]
1681 = 412 n 2 n [221]
1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)
1683 = triangular matchstick number[87]
1684 = centered triangular number [163]
1685 = 5-Knödel number [172]
1686 =
∑
k =
1
45
σ
(
k )
{\displaystyle \sum _{k=1}^{45}\sigma (k )}
[206]
1687 = 7-Knödel number[168]
1688 = number of finite connected sets of positive integers greater than one with least common multiple 72[425]
1689 =
9 ! !
∑
k =
0
4
1
2 k +
1
{\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1}}}
[426]
1690 = number of compositions of 14 into powers of 2[427]
1691 = the same upside down, which makes it a strobogrammatic number[428]
1692 = coreful perfect number[346]
1693 = smallest prime >41 2 [187]
1694 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}[150]
1695 = magic constant of n n magic square and n n Number of partitions of 58 into prime parts
1696 = sum of totient function for first 74 integers
1697 = Friedlander-Iwaniec prime[141]
1698 = number of rooted trees with 47 vertices in which vertices at the same level have the same degree[245]
1699 = number of rooted trees with 48 vertices in which vertices at the same level have the same degree[245]
1700 to 1799 [ edit ]
1700 = σ2 39 ): sum of squares of divisors of 39[298]
1701
{
8 4
}
{\displaystyle \left\{{8 \atop 4}\right\}}
Star Trek
1702 = palindromic in 3 consecutive bases: 89814 15 16
1703 = 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1[429]
1704 = sum of the squares of the parts in the partitions of 18 into two distinct parts[430]
1705 = tribonacci number [431]
1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4[432]
1707 = number of partitions of 30 in which the number of parts divides 30[319]
1708 = 22 [433]
1709 = first of a sequence of eight primes formed by adding 57
1710 = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts[155]
1711 = triangular number, centered decagonal number
1712 = number of irredundant sets in the 29-cocktail party graph[251]
1713 = number of aperiodic rooted trees with 12 nodes[434]
1714 = number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of an 3 × 6 grid of squares [435]
1715 = k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1716 = 857 + 859: sum of twin prime pair[229]
1717 = pentagonal number[112]
1718 =
∑
d
|
12
(
12 d
)
{\displaystyle \sum _{d|12}{\binom {12}{d}}}
[436]
1719 = composite de Polignac number [213]
1720 = sum of the first 31 primes
1721 = twin prime; number of squares between 422 4 [152]
1722 = Giuga number ,[437] [90]
1723 = super-prime
1724 = maximal number of regions the plane is divided into by drawing 42 circles[243]
1725 = 472 2 15 ))2 15 ))2 [438]
1726 = number of partitions of 44 into distinct and relatively prime parts[439]
1727 = area of the 24th conjoined trapezoid [207]
1728 duodecimal , that is, the cube of twelve (called a great gross ), and so, the number of cubic inches in a cubic foot , palindromic in base 11 (133111 23
1729 taxicab number , Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number . In the decimal expansion of e Hair
1730 = 3 × 242 [333]
1731 = k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1732 =
∑
k =
0
5
(
5 k
)
k
{\displaystyle \sum _{k=0}^{5}{\binom {5}{k}}^{k}}
[440]
1733 = Sophie Germain prime , palindromic in bases 3, 18, 19.
1734 = surface area of a cube of edge length 17[441]
1735 = number of partitions of 55 such that the smallest part is greater than or equal to number of parts[262]
1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18[58]
1737 = pinwheel number[133]
1738 = number of achiral integer partitions of 52[293]
1739 = number of 1s in all partitions of 30 into odd parts[442]
1740 = number of squares in the Aztec diamond of order 29[404]
1741 = super-prime , centered square number[53]
1742 = number of regions the plane is divided into by 30 ellipses[139]
1743 = wiener index of the windmill graph D(3,21)[166]
1744 = k such that k, k+1 and k+2 are sums of 2 squares[418]
1745 = 5-Knödel number [172]
1746 = number of unit-distance graphs on 8 nodes[443]
1747 = balanced prime[134]
1748 = number of partitions of 55 into distinct parts in which the number of parts divides 55[444]
1749 = number of integer partitions of 33 with no part dividing all the others[267]
1750 = hypotenuse in three different Pythagorean triangles[353]
1751 = cropped hexagone [281]
1752 = 792 2 [282]
1753 = balanced prime [134]
1754 = k such that 5*2k [280]
1755 = number of integer partitions of 50 whose augmented differences are distinct[312]
1756 = centered pentagonal number[85]
1757 = least number of triangles of the Spiral of Theodorus to complete 13 revolutions[247]
1758 =
∑
k =
1
46
σ
(
k )
{\displaystyle \sum _{k=1}^{46}\sigma (k )}
[206]
1759 = de Polignac prime[370]
1760 = the number of yards in a mile
1761 = k such that k, k+1 and k+2 are products of two primes[283]
1762 = number of binary sequences of length 12 and curling number 2 [445]
1763 = number of edges in the join of two cycle graphs, both of order 41[180]
1764 = 422
1765 = number of stacks, or planar partitions of 15[446]
1766 = number of points on surface of octahedron with edgelength 21[184]
1767 = σ(28 2 35 2 [447]
1768 = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation[448]
1769 = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts[155]
1770 = triangular number, hexagonal number,[68] Seventeen Seventy , town in Australia
1771 = tetrahedral number[153]
1772 = centered heptagonal number,[108]
1773 = number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively[449]
1774 = number of rooted identity trees with 15 nodes and 5 leaves[450]
1775 =
∑
1 ≤
i ≤
10
p r i m e (
i )
⋅
(
2 ⋅
i −
1 )
{\displaystyle \sum _{1\leq i\leq 10}prime(i )\cdot (2\cdot i-1)}
[451]
1776 = 24th square star number .[452]
1777 = smallest prime >42 2 [187]
1778 = least k >= 1 such that the remainder when 6k [453]
1779 = number of achiral integer partitions of 53[293]
1780 = number of lattice paths from (0, 0) to (7, 7) using E (1, 0) and N (0, 1) as steps that horizontally cross the diagonal y = x with even many times[454]
1781 = the first 1781 digits of e form a prime[455]
1782 = heptagonal number[107]
1783 = de Polignac prime[370]
1784 = number of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} such that every pair of distinct elements has a different quotient[456]
1785 = square pyramidal number,[56] [87]
1786 = centered triangular number [163]
1787 = super-prime , sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)
1788 = Euler transform of -1, -2, ..., -34[457]
1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)[458]
1790 = number of partitions of 50 into pairwise relatively prime parts[199]
1791 = largest natural number that cannot be expressed as a sum of at most four hexagonal numbers .
1792 = Granville number
1793 = number of lattice points inside a circle of radius 24[158]
1794 = nonagonal number,[218] [73]
1795 = number of heptagons with perimeter 38[459]
1796 = k such that geometric mean of phi(k ) and sigma(k ) is an integer[334]
1797 = number k such that phi(prime(k )) is a square[331]
1798 = 2 × 29 × 31 = 102 2 2 [460]
1799 = 2 × 302 twin square [336]
1800 to 1899 [ edit ]
1800 = pentagonal pyramidal number,[342] Achilles number , also, in da Ponte's Don Giovanni
1801 = cuban prime , sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)[416]
1802 = 2 × 302 [179] [211]
1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)[461]
1804 = number k such that k^64 + 1 is prime
1805 = number of squares between 432 4 [152]
1806 = pronic number,[90] Sylvester's sequence , primary pseudoperfect number ,[462] n n th Bernoulli number ,[463] Schröder number [464]
1807 = fifth term of Sylvester's sequence[465]
1808 = maximal number of regions the plane is divided into by drawing 43 circles[243]
1809 = sum of first 17 super-primes [466]
1810 =
∑
k =
0
4
(
4 k
)
4
{\displaystyle \sum _{k=0}^{4}{\binom {4}{k}}^{4}}
[467]
1811 = Sophie Germain prime
1812 = n such that n32 [169]
1813 = number of polyominoes with 26 cells, symmetric about two orthogonal axes[468]
1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six[469]
1815 = polygonal chain number
#
(
P
2 ,
1
3
)
{\displaystyle \#(P_{2,1}^{3})}
[470]
1816 = number of strict partions of 44[146]
1817 = total number of prime parts in all partitions of 20[471]
1818 = n such that n32 [169]
1819 = sum of the first 32 primes, minus 32[472]
1820 = pentagonal number,[112] [296] [473]
1821 = member of the Mian–Chowla sequence[57]
1822 = number of integer partitions of 43 whose distinct parts are connected[269]
1823 = super-prime , safe prime[61]
1824 = 432 2 [282]
1825 = octagonal number [186]
1826 = decagonal pyramidal number[299]
1827 = vampire number [242]
1828 = meandric number , open meandric number , appears twice in the first 10 decimal digits of e
1829 = composite de Polignac number [213]
1830 = triangular number
1831 = smallest prime with a gap of exactly 16 to next prime (1847)[474]
1832 = sum of totient function for first 77 integers
1833 = number of atoms in a decahedron with 13 shells[475]
1834 = octahedral number,[181]
1835 = absolute value of numerator of
D
6
(
5 )
{\displaystyle D_{6}^{(5 )}}
[476]
1836 = factor by which a proton is more massive than an electron
1837 = star number[126]
1838 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}[150]
1839 =
⌊
13 !
3
⌋
{\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }
[477]
1840 = 432 2 [282]
1841 = solution to the postage stamp problem with 3 denominations and 29 stamps,[478]
1842 = number of unlabeled rooted trees with 11 nodes[479]
1843 = k such that phi(k ) is a perfect cube,[480]
1844 = 37 3 [481]
1845 = number of partitions of 25 containing at least one prime,[482]
1846 = sum of first 49 composite numbers[217]
1847 = super-prime
1848 = number of edges in the join of two cycle graphs, both of order 42[180]
1849 = 432 6 [221]
1850 = Number of partitions of 59 into prime parts
1851 = sum of the first 32 primes
1852 = number of quantales on 5 elements, up to isomorphism[483]
1853 = sum of primitive roots of 27-th prime,[484]
1854 = number of permutations of 7 elements with no fixed points,[485]
1855 = rencontres number: number of permutations of [7 ] with exactly one fixed point[486]
1856 = sum of totient function for first 78 integers
1857 = Mertens function zero, pinwheel number[133]
1858 = number of 14-carbon alkanes C14 H 30 [487]
1859 = composite de Polignac number [213]
1860 = number of squares in the Aztec diamond of order 30[488]
1861 = centered square number,[53]
1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition
1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition
1864 = Mertens function zero,
1864
! −
2
2
{\displaystyle {\frac {1864!-2}{2}}}
[489]
1865 = 123456 senary metadrome (number with digits in strict ascending order in base 6)[490]
1866 = Mertens function zero, number of plane partitions of 16 with at most two rows[491]
1867 = prime de Polignac number [370]
1868 = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^[329]
1869 = Hultman number: SH [492]
1870 = decagonal number[137]
1871 = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)[493]
1872 = first Zagreb index of the complete graph K13 [332]
1873 = number of Narayana's cows and calves after 21 years[252]
1874 = area of the 25th conjoined trapezoid [207]
1875 = 502 2
1876 = number k such that k^64 + 1 is prime
1877 = number of partitions of 39 where 39 divides the product of the parts[494]
1878 = n such that n32 [169]
1879 = a prime with square index[495]
1880 = the 10th element of the self convolution of Lucas numbers[496]
1881 = tricapped prism number[497]
1882 = number of linearly separable Boolean functions in 4 variables[498]
1883 = number of conjugacy classes in the alternating group A28 [360]
1884 = k such that 5*2k [280]
1885 = Zeisel number[320]
1886 = number of partitions of 64 [499]
1887 = number of edges in the hexagonal triangle T(34 )[160]
1888 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers )[300]
1889 = Sophie Germain prime, highly cototient number[82]
1890 = triangular matchstick number[87]
1891 = triangular number, sum of 5 consecutive primes (367 + 373 + 379 + 383 + 389 ) hexagonal number,[68] [85] centered triangular number [163]
1892 = pronic number[90]
1893 = 442 44 [203]
1894 = maximal number of regions the plane is divided into by drawing 44 circles[243]
1895 = Stern-Jacobsthal number[287]
1896 = member of the Mian-Chowla sequence[57]
1897 = member of Padovan sequence,[113] [500]
1898 = smallest multiple of n whose digits sum to 26[501]
1899 = cropped hexagone [281]
1900 to 1999 [ edit ]
1900 = number of primes <= 214 [64] 1900 (film)or Novecento , 1976 movie. 1900 was the year Thorold Gosset introduced his list of semiregular polytopes ; it is also the year Max Brückner published his study of polyhedral models, including stellations of the icosahedron , such as the novel final stellation of the icosahedron .
1901 = Sophie Germain prime, centered decagonal number
1902 = number of symmetric plane partitions of 27[502]
1903 = generalized catalan number[503]
1904 = number of flat partitions of 43[352]
1905 = Fermat pseudoprime [138]
1906 = number n such that 3n [504]
1907 = safe prime,[61] [134]
1908 = coreful perfect number[346]
1909 = hyperperfect number [505]
1910 = number of compositions of 13 having exactly one fixed point[506]
1911 = heptagonal pyramidal number[189]
1912 = size of 6th maximum raising after one blind in pot-limit poker[507]
1913 = super-prime , Honaker prime[263]
1914 = number of bipartite partitions of 12 white objects and 3 black ones[508]
1915 = number of nonisomorphic semigroups of order 5[509]
1916 = sum of first 50 composite numbers[217]
1917 = number of partitions of 51 into pairwise relatively prime parts[199]
1918 = heptagonal number[107]
1919 = smallest number with reciprocal of period length 36 in base 10[510]
1920 = sum of the nontriangular numbers between successive triangular numbers
1921 = 4-dimensional centered cube number[511]
1922 = Area of a square with diagonal 62[93]
1923 = 2 × 312 [236]
1924 = 2 × 312 [179]
1925 = number of ways to write 24 as an orderless product of orderless sums[147]
1926 = pentagonal number[112]
1927 = 211 2 [512]
1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)[513]
1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected[269]
1930 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53[354]
1931 = Sophie Germain prime
1932 = number of partitions of 40 into prime power parts[246]
1933 = centered heptagonal number,[108] [263]
1934 = sum of totient function for first 79 integers
1935 = number of edges in the join of two cycle graphs, both of order 43[180]
1936 = 442 [514]
1937 = number of chiral n-ominoes in 12-space, one cell labeled[515]
1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22[184]
1939 = 7-Knödel number[168]
1940 = the Mahonian number: T(8, 9)[226]
1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines[516]
1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes[517]
1943 = largest number not the sum of distinct tetradecagonal numbers[518]
1944 = 3-smooth number (2 3 5 Achilles number [381]
1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime[519]
1946 = number of surface points on a cube with edge-length 19[58]
1947 = k such that 5·2k 2 m [520]
1948 = number of strict solid partitions of 20[129]
1949 = smallest prime >44 2 [187]
1950 =
1 ⋅
2 ⋅
3 +
4 ⋅
5 ⋅
6 +
7 ⋅
8 ⋅
9 +
10 ⋅
11 ⋅
12
{\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}
[521] [518]
1951 = cuban prime[416]
1952 = number of covers of {1, 2, 3, 4}[522]
1953 = triangular number
1954 = number of sum-free subsets of {1, ..., 16}[311]
1955 = number of partitions of 25 with at least one distinct part[237]
1956 = nonagonal number[218]
1957 =
∑
k =
0
6
6 !
k !
{\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}
[523]
1958 = number of partitions of 25[239]
1959 = Heptanacci-Lucas number[524]
1960 = number of parts in all partitions of 33 into distinct parts[84]
1961 = number of lattice points inside a circle of radius 25[158]
1962 = number of edges in the join of the complete graph K36 36 [525]
1963 ! - 1 is prime[526]
1964 = number of linear forests of planted planar trees with 8 nodes[527]
1965 = total number of parts in all partitions of 17[104]
1966 = sum of totient function for first 80 integers
1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem[528]
σ(1968) = σ(1967) + σ(1966)[529]
1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize[530]
1970 = number of compositions of two types of 9 having no even parts[531]
1971 =
3
7
−
6
3
{\displaystyle 3^{7}-6^{3}}
[532]
1972 = n such that
n
37
−
1
n −
1
{\displaystyle {\frac {n^{37}-1}{n-1}}}
[533]
1973 = Sophie Germain prime, Leonardo prime
1974 = number of binary vectors of length 17 containing no singletons[219]
1975 = number of partitions of 28 with nonnegative rank[393]
1976 = octagonal number [186]
1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons[534]
1978 = n such that n | (3 n [535]
1979 = number of squares between 452 4 [152]
1980 = pronic number[90]
1981 = pinwheel number[133]
1982 = maximal number of regions the plane is divided into by drawing 45 circles[243]
1983 = skiponacci number[159]
1984 = 11111000000 in binary , see also: 1984 (disambiguation)
1985 = centered square number [53]
1986 = number of ways to write 25 as an orderless product of orderless sums[147]
1987 prime number
1988 = sum of the first 33 primes
1989 = number of 9-step mappings with 4 inputs[301]
1990 = Stella octangula number
1991 = 11 × 181, the 46th Gullwing number,[536] [537]
1992 = number of nonisomorphic sets of nonempty subsets of a 4-set[538]
1993 = a number with the property that 41993 - 31993 is prime,[539] [148]
1994 = Glaisher's function W(37 )[540]
1995 = number of unlabeled graphs on 9 vertices with independence number 6[541]
1996 = a number with the property that (1996! + 3)/3 is prime[542]
1997 =
∑
k =
1
21
k ⋅
ϕ
(
k )
{\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k )}}
[543]
1998 = triangular matchstick number[87]
1999 = centered triangular number [544] regular forms in a myriagram .
Prime numbers [ edit ]
There are 135 prime numbers between 1000 and 2000:[545] [546]
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999
^ In the sequence of regular 1000 -gonal numbers of the form
n ×
(
499
n −
498
)
{\displaystyle n\times (499n-498)}
[13]
1
{\displaystyle 1}
n
{\displaystyle n}
1600 ,[15] Euler totient of 4000 and 6000 ,[16] [13] average of divisors that is 2997;[17] [18] ÷ 2 = 2996, and 1000 + 2997 + 5992 = 9989 (a difference of 4 from the fourth member, after 1).polygrams to the regular chiliagon: 300 are regular compound star forms — a count that represents the twenty-fourth triangular number [19] star polygons .
^ 1600 , a repdigit in septenary (44447 [23] [22] n n [24] [25] super-prime .[26] range of 777 integers (1107 : 331), which as a number is also a repdigit in senary .[27]
^ The sum (2 3 5 ... + 29 of the first 10 prime numbers is 129 , which is the 97th indexed composite number .[29] [22] super-prime ,[26] 1000 − 201 = 799 , which is the smallest number in decimal to have a digit sum of 25,[30] mirror permutation of digits of 997.99 73 172 , the one hundred and thirty-second composite, with 132 itself the 99th composite;[22] [25] 1601 is the 252nd prime,[25] 197 ,[22] lucky number of Euler n 2 n [31] [32] 1061 [33] 3 27 3 8 binary number is "1000",[34] factorial base , is equivalent to 2410 [35] In primorial base , it is equal to 3010 [36]
References [ edit ]
^ Sloane, N. J. A. (ed.). "Sequence A051876 (24-gonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m equal to 0, +1, -1, +2, -2, +3, -3, ...)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A034828 (a(n ) equal to floor(n^2/4)*(n/2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Ngaokrajang, Kival. Sloane, N. J. A. (ed.). "Illustration for n equal to 1..10 [A034828]" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Janjic, M.; Petkovic, B. (2013). "A Counting Function". pp. 14, 15. arXiv :1301.4550 math.CO ]. Bibcode :2013arXiv1301.4550J
^ Sloane, N. J. A. (ed.). "Sequence A143945 (Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A054501 (Multiplicity sequence for classification of nonattacking queens on n X n toroidal board)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A054500 (Indicator sequence for classification of nonattacking queens on n X n toroidal board)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A054502 (Counting sequence for classification of nonattacking queens on n X n toroidal board)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly . Washington, D.C.: Mathematical Association of America . 101 (7 ): 629–639. doi :10.1080/00029890.1994.11997004 JSTOR 2974691
^ Sloane, N. J. A. (ed.). "Sequence A364349 (Number of strict integer partitions of n containing the sum of no subset of the parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers: a(n ) equal to n*(499*n - 498))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Aṣiru, Muniru A. (2016). "All square chiliagonal numbers". International Journal of Mathematical Education in Science and Technology . 47 7 ). Oxfordshire: Taylor & Francis : 1123–1134. Bibcode :2016IJMES..47.1123A . doi :10.1080/0020739X.2016.1164346 . MR 3528540 . S2CID 123953958 . Zbl 1396.97005 .
^ Sloane, N. J. A. (ed.). "Sequence A048050 (Chowla's function: sum of divisors of n except for 1 and n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function phi(n ): count numbers <= n and prime to n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers n such that the average of the divisors of n is an integer: sigma_0(n ) divides sigma_1(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n ) is the binomial(n+1,2): n*(n+1)/2 equal to 0 + 1 + 2 + ... + n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function psi(n ): least k such that x^k is congruent 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002088 (Sum of totient function: a(n ) is Sum_{k equal to1..n} phi(k ), cf. A000010)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 18 December 2023 .
^ Sloane, N. J. A. (ed.). "Sequence A048332 (Numbers that are repdigits in base 7)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A028987 (Repdigit - 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A048331 (Numbers that are repdigits in base 6)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A366581 (a(n ) = phi(p(n )), where phi is Euler's totient function (A000010) and p(n ) is the number of partitions of n (A000041))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A051885 (Smallest number whose sum of digits is n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A202018 (a(n ) equal to n^2 + n + 41)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005846 (Primes of the form n^2 + n + 41)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007088 (The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007623 (Integers written in factorial base)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A049345 (n written in primorial base)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "1000" . Prime Curious!. Archived from the original on 25 March 2022.
^ Sloane, N. J. A. (ed.). "Sequence A152396 (Let f(M,k) denote the decimal concatenation of k numbers starting with M: M | M-1 | M-2 | ... | M-k+1, k greater than 1. Then a(n ) is the smallest M such that for all m in {1,..,n} an m-th prime occurs as f(M,k) for the smallest possible k, order prioritized m equal to 1 through n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A227949 (Primes obtained by concatenating decremented numbers starting at a power of 10)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Ronan, Mark (2006). Symmetry and the Monster: One of the Greatest Quests of Mathematics . New York: Oxford University Press . pp. vii, 1–255. doi :10.1007/s00283-008-9007-9 ISBN 978-0-19-280722-9 MR 2215662 . OCLC 180766312 . Zbl 1113.00002 .
^ Sloane, N. J. A. (ed.). "Sequence A001228 (Orders of sporadic simple groups)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A122189 (Heptanacci numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A332307 (Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 8 January 2023 .
^ Sloane, N. J. A. (ed.). "Sequence A036063 (Increasing gaps among twin primes: size)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A003352 (Numbers that are the sum of 7 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A061341 (A061341 Numbers not ending in 0 whose cubes are concatenations of other cubes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003353 (Numbers that are the sum of 8 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A034262 (a(n ) = n^3 + n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A020473 (Egyptian fractions: number of partitions of 1 into reciprocals of positive integers <= n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers: a(n ) = 2*n*(n+1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 10 October 2023 .
^ a b c d e f g h i j k l m n o Sloane, N. J. A. (ed.). "Sequence A005384 (Sophie Germain primes p: 2p+1 is also prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000325 (a(n ) = 2^n - n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006002 (a(n ) = n*(n+1)^2/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005897 (6*n^2 + 2 for n > 0)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A316729 (Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m = 0, +1, -1, +2, -2, +3, -3)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006313 (Numbers n such that n^16 + 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i j k l Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes p: (p-1)/2 is also prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes <= 2^n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's)... is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A004801 (Sum of 12 positive 9th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A161328 (E-toothpick sequence (see Comments lines for definition))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A023036 (Smallest positive even integer that is an unordered sum of two primes in exactly n ways)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007522 (Primes of the form 8n+7, that is, primes congruent to -1 mod 8)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 10 October 2023 .
^ a b c d Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A000695 (Moser-de Bruijn sequence: sums of distinct powers of 4)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003356 (Numbers that are the sum of 11 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A003357 (Numbers that are the sum of 12 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A036301 (Numbers whose sum of even digits and sum of odd digits are equal)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000025 (Coefficients of the 3rd-order mock theta function f(q ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A336130 (Number of ways to split a strict composition of n into contiguous subsequences all having the same sum)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A073576 (Number of partitions of n into squarefree parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers: records for a(n ) in A063741)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Base converter | number conversion" .
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003365 (Numbers that are the sum of 9 positive 6th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A045943 (Triangular matchstick numbers: 3*n*(n+1)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2 June 2022 .
^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: a(n ) = 3*n*(n-1)/2 + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003368 (Numbers that are the sum of 12 positive 6th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i j k l m Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: a(n ) = n^2 - n + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003349 (Numbers that are the sum of 4 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A001105 (a(n ) = 2*n^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003294 (Numbers k such that k^4 can be written as a sum of four positive 4th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007504 (Sum of the first n primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A127337 (Numbers that are the sum of 10 consecutive primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A035137 (Numbers that are not the sum of 2 palindromes (where 0 is considered a palindrome))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A347565 (Primes p such that A241014(A000720(p )) is +1 or -1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003325 (Numbers that are the sum of 2 positive cubes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A195162 (Generalized 12-gonal numbers: k*(5*k-4) for k = 0, +-1, +-2, ...)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006532 (Numbers whose sum of divisors is a square)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A341450 (Number of strict integer partitions of n that are empty or have smallest part not dividing all the others)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A006567 (Emirps (primes whose reversal is a different prime))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A003354 (Numbers that are the sum of 9 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A273873 (Number of strict trees of weight n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A292457 (Numbers where 7 outnumbers any other digit)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A073592 (Euler transform of negative integers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A077043 ("Three-quarter squares": a(n ) = n^2 - A002620(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000607 (Number of partitions of n into prime parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A056107 (Third spoke of a hexagonal spiral)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A025147 (Number of partitions of n into distinct parts >= 2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A033996 (8 times triangular numbers: a(n ) = 4*n*(n+1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A018900 (Sums of two distinct powers of 2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A046308 (Numbers that are divisible by exactly 7 primes counting multiplicity)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001232 (Numbers n such that 9*n = (n written backwards))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003350 (Numbers that are the sum of 5 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A003154 (Centered 12-gonal numbers. Also star numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003355 (Numbers that are the sum of 10 positive 5th powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A051682 (11-gonal (or hendecagonal) numbers: a(n ) = n*(9*n-7)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A121029 (Multiples of 9 containing a 9 in their decimal representation)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A292449 (Numbers where 9 outnumbers any other digit)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A087188 (number of partitions of n into distinct squarefree parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers: 2*n^2 + 6*n + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A002997 : Carmichael numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d e "Sloane's A001107 : 10-gonal (or decagonal) numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A319560 (Number of non-isomorphic strict T_0 multiset partitions of weight n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A028916 (Friedlander-Iwaniec primes: Primes of form a^2 + b^4)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A057732 (Numbers k such that 2^k + 3 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A046376 (Palindromes with exactly 2 palindromic prime factors (counted with multiplicity), and no other prime factors)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A002275 - OEIS" . oeis.org . Retrieved 8 March 2024 .
^ Sloane, N. J. A. (ed.). "Sequence A128455 (Numbers k such that 9^k - 2 is a prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e "Sloane's A076980 : Leyland numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A062801 (Number of 2 X 2 non-singular integer matrices with entries from {0,...,n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000096 (n*(n+3)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A057809 (Numbers n such that pi(n ) divides n.)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 23 May 2024 .
^ Van Ekeren, Jethro; Lam, Ching Hung; Möller, Sven; Shimakura, Hiroki (2021). "Schellekens' list and the very strange formula" . Advances in Mathematics 380 . Amsterdam: Elsevier : 1–34 (107567). arXiv :2005.12248 doi :10.1016/j.aim.2021.107567 . MR 4200469 . S2CID 218870375 . Zbl 1492.17027 .
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A000328" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005380" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A051026 (Number of primitive subsequences of 1, 2, ..., n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n >1 )" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A264237 (Sum of values of vertices at level n of the hyperbolic Pascal pyramid)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A033991 (n*(4*n-1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A000292 : Tetrahedral numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A185982 (Triangle read by rows: number of set partitions of n elements with k connectors)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A007534 (Even numbers that are not the sum of a pair of twin primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A050993 (5-Knödel numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006094 (Products of 2 successive primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A046368 (Products of two palindromic primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "1150 (number)" . The encyclopedia of numbers .
^ a b "Sloane's A000101 : Increasing gaps between primes (upper end)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 10 July 2016 .
^ a b "Sloane's A097942 : Highly totient numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d "Sloane's A080076 : Proth primes" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence n*(n+2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c "Sloane's A005900 : Octahedral numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ "Sloane's A069125 : a(n ) = (11*n^2 - 11*n + 2)/2" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ "1157 (number)" . The encyclopedia of numbers .
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2 June 2022 .
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A055887 (Number of ordered partitions of partitions)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A018805" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A024816 (Antisigma(n ): Sum of the numbers less than n that do not divide n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A063776 - OEIS" . oeis.org .
^ "A000256 - OEIS" . oeis.org .
^ "1179 (number)" . The encyclopedia of numbers .
^ "A000339 - OEIS" . oeis.org .
^ "A271269 - OEIS" . oeis.org .
^ "A000031 - OEIS" . oeis.org .
^ Higgins, Peter (2008). Number Story: From Counting to Cryptography 61 ISBN 978-1-84800-000-1
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b "Sloane's A042978 : Stern primes" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ "A121038 - OEIS" . oeis.org .
^ a b Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers: n*(3*n + 1)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A175654 - OEIS" . oeis.org .
^ oeis.org/A062092
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A024916 (Sum_1^n sigma(k ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
^ "A265070 - OEIS" . oeis.org .
^ "1204 (number)" . The encyclopedia of numbers .
^ a b Sloane, N. J. A. (ed.). "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A303815 - OEIS" . oeis.org .
^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A098237 (Composite de Polignac numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A337070 (Number of strict chains of divisors starting with the superprimorial A006939(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Higgins, ibid.
^ Sloane, N. J. A. (ed.). "Sequence A000070 (Sum_{0..n} A000041(k ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b Sloane, N. J. A. (ed.). "Sequence A006355 (Number of binary vectors of length n containing no singletons)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A001110 : Square triangular numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d e "Sloane's A016754 : Odd squares: a(n ) = (2n+1)^2. Also centered octagonal numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A303815 (Generalized 29-gonal (or icosienneagonal) numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A249911 (60-gonal (hexacontagonal) numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A004111 - OEIS" . oeis.org .
^ "A061262 - OEIS" . oeis.org .
^ a b c Sloane, N. J. A. (ed.). "Sequence A008302 (Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product{0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A006154 - OEIS" . oeis.org .
^ "A000045 - OEIS" . oeis.org .
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A160160 - OEIS" . oeis.org .
^ "Sloane's A005898 : Centered cube numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ oeis.org/A305843
^ "A007690 - OEIS" . oeis.org .
^ "Sloane's A033819 : Trimorphic numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A144300 (Number of partitions of n minus number of divisors of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000837 (Number of partitions of n into relatively prime parts. Also aperiodic partitions.)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A000041 (a(n ) is the number of partitions of n (the partition numbers))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A193757 (Numbers which can be written with their digits in order and using only a plus and a squaring operator)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b "Sloane's A002182 : Highly composite numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d e "Sloane's A014575 : Vampire numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A070169 (Rounded total surface area of a regular tetrahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A003238 (Number of rooted trees with n vertices in which vertices at the same level have the same degree)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A023894 (Number of partitions of n into prime power parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A072895 (Least k for the Theodorus spiral to complete n revolutions)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A100040 (2*n^2 + n - 5)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A051349 (Sum of first n nonprimes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A033286 (n * prime(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A084849 (1 + n + 2*n^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001792 ((n+2)*2^(n-1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A216492 (Number of inequivalent connected planar figures that can be formed from n 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007318 (Pascal's triangle read by rows)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A014574 (Average of twin prime pairs)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A173831 (Largest prime < n^4)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006872 (Numbers k such that phi(k ) equals phi(sigma(k )))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A014285 (Sum_{1..n} j*prime(j ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A071400 (Rounded volume of a regular octahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A003114 (Number of partitions of n into parts 5k+1 or 5k+4)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k ) such that sum of digits of P(k ) equals sum of digits of k)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A124826 - OEIS" . oeis.org .
^ "A142005 - OEIS" . oeis.org .
^ a b Sloane, N. J. A. (ed.). "Sequence A338470 (Number of integer partitions of n with no part dividing all the others)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A066186 - OEIS" . oeis.org .
^ a b c d Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A115073 - OEIS" . oeis.org .
^ "A061256 - OEIS" . oeis.org .
^ "A061954 - OEIS" . oeis.org .
^ Sloane, N. J. A. (ed.). "Sequence A057465 (Numbers k such that k^512 + 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A030299 - OEIS" . oeis.org .
^ a b "Sloane's A002559 : Markoff (or Markov) numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b Sloane, N. J. A. (ed.). "Sequence A005894 (Centered tetrahedral numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A018806 (Sum of gcd(x, y))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A018227 (Magic numbers: atoms with full shells containing any of these numbers of electrons are considered electronically stable)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A005064 - OEIS" . oeis.org .
^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A090781 (Numbers that can be expressed as the difference of the squares of primes in just one distinct way)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A056809 (Numbers k such that k, k+1 and k+2 are products of two primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A316473 - OEIS" . oeis.org .
^ "A000032 - OEIS" . oeis.org .
^ "1348 (number)" . The encyclopedia of numbers .
^ a b Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A064228 (From Recamán's sequence (A005132): values of n achieving records in A057167)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A057167 (Term in Recamán's sequence A005132 where n appears for first time, or -1 if n never appears)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A064227 (From Recamán's sequence (A005132): record values in A057167)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A000603" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000960 (Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e Sloane, N. J. A. (ed.). "Sequence A330224 (Number of achiral integer partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001610 (a(n-1) + a(n-2) + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers: L(n-1) + L(n-2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A005578 (Arima sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A001157 (sigma_2(n ): sum of squares of divisors of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "A001631 - OEIS" . oeis.org . Retrieved 25 June 2023 .
^ Sloane, N. J. A. (ed.). "Sequence A088274 (Numbers k such that 10^k + 7 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000111 (Euler or up/down numbers: e.g.f. sec(x ) + tan(x ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002414 (Octagonal pyramidal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A001567 : Fermat pseudoprimes to base 2" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ "Sloane's A050217 : Super-Poulet numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A054552 (4*n^2 - 3*n + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A017919 (Powers of sqrt(5 ) rounded down)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A109308 (Lesser emirps (primes whose digit reversal is a larger prime))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A325349 (Number of integer partitions of n whose augmented differences are distinct)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A051400 (Smallest value of x such that M(x ) equals n, where M() is Mertens's function A002321)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A000682 : Semimeanders" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A002445 (Denominators of Bernoulli numbers B_{2n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A045918 (Describe n. Also called the "Say What You See" or "Look and Say" sequence LS(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A050710 (Smallest composite that when added to sum of prime factors reaches a prime after n iterations)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A067538 (Number of partitions of n in which the number of parts divides n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b "Sloane's A051015 : Zeisel numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b c Sloane, N. J. A. (ed.). "Sequence A059845 (n*(3*n + 11)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000097 (Number of partitions of n if there are two kinds of 1's and two kinds of 2's)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A061068 (Primes which are the sum of a prime and its subscript)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001764 (binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A000108 : Catalan numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ a b Sloane, N. J. A. (ed.). "Sequence A071399 (Rounded volume of a regular tetrahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c Sloane, N. J. A. (ed.). "Sequence A006832 (Discriminants of totally real cubic fields)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A003037 (Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005259 (Apery (Apéry) numbers: Sum_0^n (binomial(n,k)*binomial(n+k,k))^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A062325 (Numbers k for which phi(prime(k )) is a square)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A011379 (n^2*(n+1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A005918 (Number of points on surface of square pyramid: 3*n^2 + 2 (n>0))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A011257 (Geometric mean of phi(n ) and sigma(n ) is an integer)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A056220 (2*n^2 - 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A028569 (n*(n + 9))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A071398 (Rounded total surface area of a regular icosahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A085831 (Sum_1^{2^n} d(k ) where d(k ) is the number of divisors of k (A000005))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A064410 (Number of partitions of n with zero crank)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A075207 (Number of polyhexes with n cells that tile the plane by translation)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b "Sloane's A002411 : Pentagonal pyramidal numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A015128 (Number of overpartitions of n: an overpartition of n is an ordered sequence of nonincreasing integers that sum to n, where the first occurrence of each integer may be overlined)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006578 (Triangular numbers plus quarter squares: n*(n+1)/2 + floor(n^2/4) (i.e., A000217(n ) + A002620(n )))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A098859 (Number of partitions of n into parts each of which is used a different number of times)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A097979 (Total number of largest parts in all compositions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A000078 : Tetranacci numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A114411 (Triple primorial n###)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A084647 (Hypotenuses for which there exist exactly 3 distinct integer triangles)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A002071 (Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A325325 (Number of integer partitions of n with distinct differences between successive parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A325858 (Number of Golomb partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A018000 (Powers of cube root of 9 rounded down)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A062198 (Sum of first n semiprimes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A038147 (Number of polyhexes with n cells)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A000702 (number of conjugacy classes in the alternating group A_n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001970 (Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A071396 (Rounded total surface area of a regular octahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000084 (Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000615 (Threshold functions of exactly n variables)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A100129 (Numbers k such that 2^k starts with k)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000057 (Primes dividing all Fibonacci sequences)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A319066 (Number of partitions of integer partitions of n where all parts have the same length)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A056327 (Number of reversible string structures with n beads using exactly three different colors)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002720 (Number of partial permutations of an n-set; number of n X n binary matrices with at most one 1 in each row and column)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c d Sloane, N. J. A. (ed.). "Sequence A065381 (Primes not of the form p + 2^k)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A140090 (n*(3*n + 7)/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A169942 (Number of Golomb rulers of length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A169952 (Second entry in row n of triangle in A169950)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A034962 (Primes that are the sum of three consecutive primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A046386 (Products of four distinct primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A127106 (Numbers n such that n^2 divides 6^n-1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A008406 (Triangle T(n,k) read by rows, giving number of graphs with n nodes and k edges))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A057660 (Sum_{1..n} n/gcd(n,k))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A088319 (Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A052486 (Achilles numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A056995 (Numbers k such that k^256 + 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A005231 : Odd abundant numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A056026 (Numbers k such that k^14 is congruent with 1 (mod 15^2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A076409 (Sum of the quadratic residues of prime(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A070142 (Numbers n such that [A070080(n ), A070081(n ), A070082(n )] is an integer triangle with integer area)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A033428 (3*n^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A071402 (Rounded volume of a regular icosahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A326123 (a(n ) is the sum of all divisors of the first n odd numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006327 (Fibonacci(n ) - 3. Number of total preorders)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A000045 : Fibonacci numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A100145 (Structured great rhombicosidodecahedral numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A023360 (Number of compositions of n into prime parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A103473 (Number of polyominoes consisting of 7 regular unit n-gons)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007584 (9-gonal (or enneagonal) pyramidal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A022004 (Initial members of prime triples (p, p+2, p+6))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006489 (Numbers k such that k-6, k, and k+6 are primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A213427 (Number of ways of refining the partition n^1 to get 1^n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A134602 (Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A084990 (n*(n^2+3*n-1)/3)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A077068 (Semiprimes of the form prime + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A115160 (Numbers that are not the sum of two triangular numbers and a fourth power)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A046092 (4 times triangular numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005382 (Primes p such that 2p-1 is also prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001339 (Sum_{0..n} (k+1)! binomial(n,k))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007290 (2*binomial(n,3))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A058360 (Number of partitions of n whose reciprocal sum is an integer)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A046931 (Prime islands: least prime whose adjacent primes are exactly 2n apart)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A001599 : Harmonic or Ore numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A056613 (Number of n-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A068140 (Smaller of two consecutive numbers each divisible by a cube greater than one)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A030272 (Number of partitions of n^3 into distinct cubes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A018818 (Number of partitions of n into divisors of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A071401 (Rounded volume of a regular dodecahedron with edge length n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b c "Sloane's A002407 : Cuban primes" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A082982 (Numbers k such that k, k+1 and k+2 are sums of 2 squares)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A057562 (Number of partitions of n into parts all relatively prime to n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A261983 (Number of compositions of n such that at least two adjacent parts are equal)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A053781 (Numbers k that divide the sum of the first k composite numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A140480 (RMS numbers: numbers n such that root mean square of divisors of n is an integer)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A023108 (Positive integers which apparently never result in a palindrome under repeated applications of the function A056964(x ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A286518 (Number of finite connected sets of positive integers greater than one with least common multiple n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A004041 (Scaled sums of odd reciprocals: (2*n + 1)!!*(Sum_{0..n} 1/(2*k + 1)))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A023359 (Number of compositions (ordered partitions) of n into powers of 2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000787 (Strobogrammatic numbers: the same upside down)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A224930 (Numbers n such that n divides the concatenation of all divisors in descending order)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A294286 (Sum of the squares of the parts in the partitions of n into two distinct parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A000073 : Tribonacci numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A020989 ((5*4^n - 2)/3)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A331378 (Numbers whose product of prime indices is divisible by their sum of prime factors)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A301700 (Number of aperiodic rooted trees with n nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A331452 (number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A056045 ("Sum_{d divides n}(binomial(n,d))")" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A007850 : Giuga numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A161757 ((prime(n ))^2 - (nonprime(n ))^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A078374 (Number of partitions of n into distinct and relatively prime parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A167008 (Sum_{0..n} C(n,k)^k)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A033581 (6*n^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A350507 (Number of (not necessarily connected) unit-distance graphs on n nodes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A102627 (Number of partitions of n into distinct parts in which the number of parts divides n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A216955 (number of binary sequences of length n and curling number k)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001523 (Number of stacks, or planar partitions of n; also weakly unimodal compositions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A065764 (Sum of divisors of square numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A220881 (Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals up to rotation)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A154964 (3*a(n-1) + 6*a(n-2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A055327 (Triangle of rooted identity trees with n nodes and k leaves)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A316322 (Sum of piles of first n primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A045944 (Rhombic matchstick numbers: n*(3*n+2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A127816 (least k such that the remainder when 6^k is divided by k is n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005317 ((2^n + C(2*n,n))/2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A064118 (Numbers k such that the first k digits of e form a prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A325860 (Number of subsets of {1..n} such that every pair of distinct elements has a different quotient)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A073592 (Euler transform of negative integers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A025047 (Alternating compositions, i.e., compositions with alternating increases and decreases, starting with either an increase or a decrease)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A288253 (Number of heptagons that can be formed with perimeter n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A235488 (Squarefree numbers which yield zero when their prime factors are xored together)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A075213 (Number of polyhexes with n cells that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A054377 : Primary pseudoperfect numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Kellner, Bernard C.; 'The equation denom(B n n
^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 22 May 2016 .
^ "Sloane's A000058 : Sylvester's sequence" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A083186 (Sum of first n primes whose indices are primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005260 (Sum_{0..n} binomial(n,k)^4)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A056877 (Number of polyominoes with n cells, symmetric about two orthogonal axes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A061801 ((7*6^n - 2)/5)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A152927 (Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 1 as k varies)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A037032 (Total number of prime parts in all partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A101301 (The sum of the first n primes, minus n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2 June 2022 .
^ Sloane, N. J. A. (ed.). "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A004068 (Number of atoms in a decahedron with n shells)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001905 (From higher-order Bernoulli numbers: absolute value of numerator of D-number D2n(2n-1))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A214083 (floor(n!^(1/3)))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A001208 (solution to the postage stamp problem with 3 denominations and n stamps)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000081 (Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A039771 (Numbers k such that phi(k ) is a perfect cube)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A024026 (3^n - n^3)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A235945 (Number of partitions of n containing at least one prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A354493 (Number of quantales on n elements, up to isomorphism)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A088144 (Sum of primitive roots of n-th prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000166 (Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000240 (Rencontres numbers: number of permutations of [n] with exactly one fixed point)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000602 (Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n )H(2n+2) ignoring stereoisomers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ " . Retrieved 20 September 2022 .
^ Sloane, N. J. A. (ed.). "Sequence A082671 (Numbers n such that (n!-2)/2 is a prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A023811 (Largest metadrome (number with digits in strict ascending order) in base n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000990 (Number of plane partitions of n with at most two rows)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A164652 (Hultman numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A057568 (Number of partitions of n where n divides the product of the parts)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A011757 (prime(n^2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A004799 (Self convolution of Lucas numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005920 (Tricapped prism numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000609 (Number of threshold functions of n or fewer variables)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A259793 (Number of partitions of n^4 into fourth powers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002998 (Smallest multiple of n whose digits sum to n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005987 (Number of symmetric plane partitions of n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A023431 (Generalized Catalan Numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A217135 (Numbers n such that 3^n - 8 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A034897 : Hyperperfect numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A240736 (Number of compositions of n having exactly one fixed point)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A007070 (4*a(n-1) - 2*a(n-2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000412 (Number of bipartite partitions of n white objects and 3 black ones)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A027851 (Number of nonisomorphic semigroups of order n)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A003060 (Smallest number with reciprocal of period length n in decimal (base 10))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A008514 (4-dimensional centered cube numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A024012 (2^n - n^2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002845 (Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ "Sloane's A051870 : 18-gonal numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 12 June 2016 .
^ Sloane, N. J. A. (ed.). "Sequence A045648 (Number of chiral n-ominoes in (n-1)-space, one cell labeled)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000127 (Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A178084 (Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ a b Sloane, N. J. A. (ed.). "Sequence A007419 (Largest number not the sum of distinct n-th-order polygonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A100953 (Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A226366 (Numbers k such that 5*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A319014 (1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + ... + (up to n))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A055621 (Number of covers of an unlabeled n-set)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000522 (Total number of ordered k-tuples of distinct elements from an n-element set)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A104621 (Heptanacci-Lucas numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A030238 (Backwards shallow diagonal sums of Catalan triangle A009766)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A089046 (Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A065900 (Numbers n such that sigma(n ) equals sigma(n-1) + sigma(n-2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Jon Froemke & Jerrold W. Grossman (February 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?" . The American Mathematical Monthly 100 (2 ). Mathematical Association of America: 180–183. doi :10.2307/2323780 . JSTOR 2323780 .
^ Sloane, N. J. A. (ed.). "Sequence A052542 (2*a(n-1) + a(n-2))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A024069 (6^n - n^7)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A217076 (Numbers n such that (n^37-1)/(n-1) is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A302545 (Number of non-isomorphic multiset partitions of weight n with no singletons)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A277288 (Positive integers n such that n divides (3^n + 5))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A187220 (Gullwing sequence)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A046351 (Palindromic composite numbers with only palindromic prime factors)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A000612 (Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ OEIS : A059801
^ Sloane, N. J. A. (ed.). "Sequence A002470 (Glaisher's function W(n ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A263341 (Triangle read by rows: T(n,k) is the number of unlabeled graphs on n vertices with independence number k)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A089085 (Numbers k such that (k! + 3)/3 is prime)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A011755 (Sum_{1..n} k*phi(k ))" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture" . wstein.org . Retrieved 6 February 2021 .
t
e
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000
R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=1000_(number)&oldid=1233256335#1900_to_1999 " C a t e g o r y : ● I n t e g e r s H i d d e n c a t e g o r i e s : ● A r t i c l e s w i t h s h o r t d e s c r i p t i o n ● S h o r t d e s c r i p t i o n i s d i f f e r e n t f r o m W i k i d a t a ● U s e d m y d a t e s f r o m J a n u a r y 2 0 2 3 ● S h o r t d e s c r i p t i o n m a t c h e s W i k i d a t a ● C o m m o n s c a t e g o r y l i n k f r o m W i k i d a t a ● A r t i c l e s w i t h J 9 U i d e n t i f i e r s ● A r t i c l e s w i t h L C C N i d e n t i f i e r s
● T h i s p a g e w a s l a s t e d i t e d o n 8 J u l y 2 0 2 4 , a t 0 3 : 4 1 ( U T C ) . ● T e x t i s a v a i l a b l e u n d e r t h e C r e a t i v e C o m m o n s A t t r i b u t i o n - S h a r e A l i k e L i c e n s e 4 . 0 ;
a d d i t i o n a l t e r m s m a y a p p l y . B y u s i n g t h i s s i t e , y o u a g r e e t o t h e T e r m s o f U s e a n d P r i v a c y P o l i c y . W i k i p e d i a ® i s a r e g i s t e r e d t r a d e m a r k o f t h e W i k i m e d i a F o u n d a t i o n , I n c . , a n o n - p r o f i t o r g a n i z a t i o n . ● P r i v a c y p o l i c y ● A b o u t W i k i p e d i a ● D i s c l a i m e r s ● C o n t a c t W i k i p e d i a ● C o d e o f C o n d u c t ● D e v e l o p e r s ● S t a t i s t i c s ● C o o k i e s t a t e m e n t ● M o b i l e v i e w
[206]
, where 
is the number of partions of 
[216]
[256]
, average of a twin prime pair[257]
[260]
,[206] Mertens function zero
[206]
[309]
[330]
, where 
= number of divisors of 
: triangular number plus quarter square (i.e., A000217(44) + A002620(44))[344]
[357]
= number of cards needed to build a 31-tier house of cards with a flat, one-card-wide roof[371]
[379]
and 
[380]
[206]
= number of monotonic triples (x,y,z) in {1,2,...,16}3[401]
[406]
[206]
[426]
, decagonal number, hull number of the U.S.S. Enterprise on Star Trek
[436]
[440]
[206]
: sum of piles of first 10 primes[451]
[467]
[470]
[476]![{\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0943f39851d7f678812a33ee092226567c63e4)
[477]
is a prime[489]
,[521] largest number not the sum of distinct pentadecagonal numbers[518]
= total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set[523]
[532]
is prime[533]
[543]
where 
is the path graph on four vertices.[7]Aconnected graph with a given Wiener index represents the sum of the distances between all unordered pairsofvertices in said graph.
, the first non-trivial solution is 2997.[13] In Chowla's function, that counts the sum of divisors except for 
and 
, 2997 is the first number to have a value of 1600,[15] which is the Euler totientof4000 and 6000,[16] while the fifth member in the sequence 9985 (that follows 0, 1, 1000, 2997 and 5992)[13] has an average of divisors that is 2997;[17][18] with 5992 ÷ 2 = 2996, and 1000 + 2997 + 5992 = 9989 (a difference of 4 from the fourth member, after 1).
!["Illustration for n equal to 1..10 [A034828]"](https://oeis.org/A034828/a034828.jpg){kind=link}