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 A145041 #13 Oct 19 2024 08:35:06
%S A145041 5,17,89,521,4253,9689,9941,11213,19937,21701,859433,1398269,2976221,
%T A145041 3021377,6972593,32582657,43112609,57885161
%N A145041 Primes p (A000043) such that 2^p-1 is prime (A000668) and congruent to 31 mod 6!.
%C A145041 Mersenne numbers (with the exception of the first two) are congruent to 31, 127, 271, 607 mod 6!. This sequence is a subsequence of A000043.
%t A145041 p = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 43112609}; a = {}; Do[If[Mod[2^p[[n]] - 1, 6! ] == 31, AppendTo[a, p[[n]]]], {n, 1, Length[p]}]; a
%t A145041 Select[MersennePrimeExponent[Range[48]], PowerMod[2, #, 720] == 32 &] (* _Amiram Eldar_, Oct 19 2024 *)
%Y A145041 Cf. A000043, A000668, A124477, A139484, A145038, A112633, A145041, A145042, A145044, A145045, A145046.
%K A145041 nonn,more
%O A145041 1,1
%A A145041 _Artur Jasinski_, Sep 30 2008
%E A145041 a(18) from _Amiram Eldar_, Oct 19 2024