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It is quite a while well known (is it?) that numbers, as also Alexander Adam wrote: "because the universe of (natural) numbers is similar to an enigma" and others said, are perhaps more then 'just' numbԑrs - let say similar to atoms, which composite matter. For instance well known number 23. Is it a Ramanujan prime or not? No, this one is not: A104272. But nevertheless, why in the end it should or it should not be? So, it is 6-th non-Ramanujan prime: A174635. Number theory probably does not ask questions like: "Why 23 is non-Ramanujan prime, and not Ramanujan one?", although Hardy's school is perhaps still much alive. But in the Balthazar's upside-down (inside-out) city of M (ver. U-DI-OCM) taxi cabs use car plates as simply ʍʇ32: A011541, and so professor Balthazar's taxi cab numbers are: 2, 9271, 91393578, 8429032743696, 96426967295688984, 44356021345218591335142, ... Of course, normally we would call them simply reversal taxi cab numbers, although prof. Balthazar was quite ingenuous old geek, and also this masterpiece of cartoon from Zagreb drawing school was unfortunately probably unknown outside the old ex-state.
It is also well known that 23 is (after number 2) the second prime which is not a member of twin primes (A001097, A007510), or the smallest odd non twin prime. Sometimes 'smaller' can be handy, if not for nothing, at least it can be easily remembered. Regarding remembering of numbers here's an interesting allegeable story. Famous Slovene mathematician France Križanič, who lectured mathematical calculus, once wrote . This seemed fascinating to students who knew only as much digits as TI-30 could show. Križanič in his style was silenced a while, and afterwards he explained: "It is very simple. Two point seven," and shows, "you know all. The same year Goya died," and shows first 1828, "Tolstoy was born," and shows the other 1828. "And after that some short multiplication follows," and shows to 45 90 45. But what about the 42-nd twin prime or
-th? Term a(42) can be easily find here to be 419. Some say, if an algorythm for computing the 4398046511104-th twin prime does not exits, there might be a 'computer' (think for example to one from Adams' The Hitchhiker's Guide to the Galaxy somewhere (DTorE), or let say in akashic space). If you have a black boxlike computer from Akasha, you would just type in (like in Maple's worksheet or in some OS's command line) 4398046511104 Өts0ps:tpѲ or something like that, and you would 'get' an answer instantly... In SF answԑrs are very often (again) numbԑrs - like 42.
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1 |
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87 |
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12326 |
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1 |
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39 |
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4203 |
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1 |
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20 |
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1970 |
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1 |
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19 |
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1396 |
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0 |
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8 |
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467 |
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1 |
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9 |
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636 |
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0 |
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3 |
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97 |
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1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | ... | A000027 |
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1 | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | ... | A008578 |
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1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | ... | A171622 |
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0 | 0 | 0 | 1 | 2 | 5 | 6 | 1 | 1 | 3 | 7 | 7 | 11 | 13 | 13 | 15 | 2 | 5 | 4 | 7 | 8 | 7 | 10 | 11 | 14 | 19 | 20 | ... | A004650 |
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(-1) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | #-- |
- | 3 | 3 | 7 | 8 | 7 | 4 | 5 | 9 | 9 | / | / | / | / | / | ||
(3) | 1 | 5 | 9 | 9 | 8 | 6 | 1 | 7 | 2 | 9 | 0 | 9 | 2 | 5 | A055199 | |
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- | 2 | 2 | 2 | 1 | 1 | 2 | 4 | 2 | 7 | / | / | / | / | / | |
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- | 4 | 8 | 6 | 7 | 5 | 0 | 6 | 6 | 1 | / | / | / | / | / |
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0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | ... | #-- |
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(0) | 4 | 25 | 168 | 1229 | 9592 | 78498 | 664579 | 5761455 | 50847534 | 455052511 | 4118054813 | 37607912018 | 346065536839 | 3204941750802 | 29844570422669 | ... | A006880 |
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(0) | 2 | 13 | 87 | 619 | 4808 | 39322 | 332398 | 2880950 | 25424042 | 227529235 | 2059034532 | 18803987677 | 173032827655 | 1602470967129 | 14922285687184 | ... | A091099 |
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(0) | 2 | 12 | 81 | 610 | 4784 | 39176 | 332181 | 2880505 | 25423492 | 227523276 | 2059020281 | 18803924341 | 173032709184 | 1602470783673 | 14922284735485 | ... | |
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(0) | 0 | 1 | 6 | 9 | 24 | 146 | 217 | 445 | 550 | 5959 | 14251 | 63336 | 118471 | 183456 | 951699 | ... |
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5.3923174227787602888957082611796473174008410336586218441330443786114190766565515490201414740882990271 ... | [5; 2, 1, 1, 4, 1, 1, 1, 1, 5, 2, 8, 1, 7, 1, 10, 2, 1, ...] |
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3.4021735027328796971674554214252185723660569747261239072396475211185714000837270158954736778869607218 ... | [3; 2, 2, 18, 287, 1, 8, 3, 1, 4, 1, 3, 1, 2, 1, 9, 39, 2, 1, 2, ...] |
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2.3223447076815459025679892735823779562110172616637607876882689303072864464622987700196696393392623891 ... | [2; 3, 9, 1, 3, 1, 1, 34, 3, 1, 3, 1, 5, 5, 1, 2, 1, 1, 2, 5, 1, 2, ...] |
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1.2931449416748841651796503304996953819299473677816938079981047064680830296890449755399151165006098272 ... | [1; 3, 2, 2, 3, 6, 1, 6, 1, 3, 12, 10, 1, 4, 1, 1, 1, 1, 8, 3, 7, ...] |
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1.1920511922155704915707878897888844984631928094436115325615969431904119406383487244100337567415074444 ... | [1; 5, 4, 1, 4, 1, 23, 1, 2, 2, 1, 3, 1, 2, 1, 3, 3, 1, 1, 2, 1, 2, ...] |
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1.0064890491274204382468417950335949430615664633988939892971150146932660472161695672404105311456784088 ... | [1; 154, 9, 2, 4, 1, 5, 1, 1, 1, 13, 5, 1, 1, 42, 2, 2, 2, 6, 1, ... ] |