This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A145731 #14 Jul 29 2020 22:52:14 %S A145731 4,10,19,23,24,25,27,28,30,31,32,33,34,42,48,51,52,53,55,59,60,61,62, %T A145731 68,69,71,72,74,75,76,77,78,80,81,82,84,85,86,91,92,93,95,96,98,99, %U A145731 100,101,102,103,104,105,106,109,110,112,113,115,116,117,118,119,120,121 %N A145731 Conjectured integers m such that |A144912(2, p^m)| > 0 for all Mersenne prime exponents p > 7. %C A145731 An integer m is excluded from the sequence iff A144912(2, p^m) = 0 for some Mersenne prime exponent p > 7. %C A145731 The given terms are sufficient to identify the Mersenne prime exponents 13, 17, 19 and 31 without error, followed by the incorrect 41 and 59, correct 61, incorrect 71 and correct 89. Additional terms quickly reduce the number of false positives such that, for example, the first thirty Mersenne primes can be identified within minutes using unexceptional software and hardware and, in particular, without primality testing of integers larger than 132049. %C A145731 Noting that A144912(2, k) is a function of k in base 2, it is expected that extremely efficient methods can be found for producing Mersenne primes and perfect numbers within seconds. %Y A145731 Cf. A000040, A000043, A000396, A000668, A144912. %K A145731 nonn %O A145731 1,1 %A A145731 _Reikku Kulon_, Oct 17 2008 %E A145731 Name changed and incorrect term 79 removed by _Jinyuan Wang_, Jul 29 2020