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Search: a128068 -id:a128068
Displaying 1-8 of 8 results found. page 1
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A128066 Numbers k such that (3^k + 4^k)/7 is prime. +10
17
3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
LINKS
Table of n, a(n) for n=1..16.
Henri Lifchitz & Renaud Lifchitz, Top probable primes of the form (4^p+3^p)/7
MAPLE
a:=proc(n) if type((3^n+4^n)/7, integer)=true and isprime((3^n+4^n)/7)=true then n else fi end: seq(a(n), n=1..1500); # Emeric Deutsch, Feb 17 2007
MATHEMATICA
Do[ p=Prime[n]; f=(3^p+4^p)/(4+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) f(n)=(3^n + 4^n)/7;
forprime(n=3, 10^5, if(ispseudoprime(f(n)), print1(n, ", ")))
/* Joerg Arndt, Mar 27 2011 */
CROSSREFS
Cf. A007658 = n such that (3^n + 1)/4 is prime; A057469 ((3^n + 2^n)/5); A122853 ((3^n + 5^n)/8).
Cf. A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075.
Cf. A059801 (4^n - 3^n); A121877 ((5^n - 3^n)/2).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
3 more terms from Emeric Deutsch, Feb 17 2007
2 more terms from Farideh Firoozbakht, Apr 16 2007
Two more terms (13463 and 23929) found by Lelio R Paula in 2008 corresponding to probable primes with 8105 and 14406 digits. Jean-Louis Charton, Oct 06 2010
Two more terms (81223 and 121271) found by Jean-Louis Charton in March 2011 corresponding to probable primes with 48901 and 73012 digits
STATUS
approved
A128071 Numbers k such that (3^k + 13^k)/16 is prime. +10
12
3, 7, 127, 2467, 3121, 34313 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(4) is certified prime by primo; a(5) is a probable prime. - Ray G. Opao, Aug 02 2007
a(7) > 10^5. - Robert Price, Apr 14 2013
LINKS
Table of n, a(n) for n=1..6.
MATHEMATICA
k=13; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) is(n)=isprime((3^n+13^n)/16) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128069, A128070, A128072, A128073, A128074, A128075. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
One more term from Ray G. Opao, Aug 02 2007
a(6) from Robert Price, Apr 14 2013
STATUS
approved
A128075 Numbers k such that (3^k + 19^k)/22 is prime. +10
12
3, 61, 71, 109, 9497, 36007, 50461, 66919 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(9) > 10^5. - Robert Price, Jul 21 2013
LINKS
Table of n, a(n) for n=1..8.
MATHEMATICA
k=19; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 9592} ]
PROG
(PARI) is(n)=isprime((3^n+19^n)/22) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
a(5)-a(8) from Robert Price, Jul 21 2013
STATUS
approved
A128072 Numbers k such that (3^k + 14^k)/17 is prime. +10
10
3, 7, 71, 251, 1429, 2131, 2689, 36683, 60763 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(10) > 10^5. - Robert Price, Apr 20 2013
LINKS
Table of n, a(n) for n=1..9.
MATHEMATICA
k=14; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) is(n)=isprime((3^n+14^n)/17) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128073, A128074, A128075.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
3 more terms from Ryan Propper, Jan 28 2008
a(8)-a(9) from Robert Price, Apr 20 2013
STATUS
approved
A128073 Numbers k such that (3^k + 16^k)/19 is prime. +10
10
5, 17, 61, 673, 919, 2089, 86939 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(8) > 10^5 - Robert Price, Jun 29 2013
LINKS
Table of n, a(n) for n=1..7.
MATHEMATICA
k=16; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) is(n)=isprime((3^n+16^n)/19) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128070, A128071, A128072, A128074, A128075.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
a(5) from Alexander Adamchuk, Feb 14 2007
a(6) and a(7) from Robert Price, Jun 29 2013
STATUS
approved
A128067 Numbers k such that (3^k + 7^k)/10 is prime. +10
9
3, 13, 31, 313, 3709, 7933, 14797, 30689, 38333 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(10) > 10^5. - Robert Price, Oct 03 2012
LINKS
Table of n, a(n) for n=1..9.
MATHEMATICA
k=7; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) is(n)=isprime((3^n+7^n)/10) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
More terms from Ryan Propper, Apr 02 2007
a(7)-a(9) from Robert Price, Oct 03 2012
STATUS
approved
A128069 Numbers k such that (3^k + 10^k)/13 is prime. +10
9
3, 19, 31, 101, 139, 167, 1097, 43151, 60703, 90499 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
Next term is greater than 6700. - Stefan Steinerberger, May 11 2007
a(11) > 10^5. - Robert Price, Jan 15 2013
LINKS
Table of n, a(n) for n=1..10.
MATHEMATICA
k=10; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) is(n)=isprime((3^n+10^n)/13) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128070, A128071, A128072, A128073, A128074, A128075. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
a(7) from Alexander Adamchuk, Feb 14 2007
a(8)-a(10) from Robert Price, Jan 15 2013
STATUS
approved
A128070 Numbers k such that (3^k + 11^k)/14 is prime. +10
9
3, 103, 271, 523, 23087, 69833 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(7) > 10^5. - Robert Price, Mar 04 2013
LINKS
Table of n, a(n) for n=1..6.
MATHEMATICA
k=11; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n, 1, 100} ]
PROG
(PARI) is(n)=isprime((3^n+11^n)/14) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A007658 (numbers k such that (3^k + 1)/4 is prime).
Cf. A057469 (numbers k such that (3^k + 2^k)/5 is prime).
Cf. A122853 (numbers k such that (3^k + 5^k)/8 is prime).
Cf. A128066, A128067, A128068, A128069, A128071, A128072, A128073, A128074, A128075.
Cf. A059801 (numbers k such that 4^k - 3^k is prime).
Cf. A121877 (numbers k such that (5^k - 3^k)/2 is prime).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
EXTENSIONS
a(5)-a(6) from Robert Price, Mar 04 2013
STATUS
approved
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Last modified July 26 00:14 EDT 2024. Contains 374615 sequences. (Running on oeis4.)