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%I #9 Sep 04 2023 16:35:51
%S 7,19,31,127,607,1279,2203,4423,110503,216091,1257787,20996011,
%T 24036583
%N Primes p (A000043) such that 2^p-1 is prime (A000668) and congruent to 127 mod 6!.
%C 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 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! ] == 127, AppendTo[a, p[[n]]]], {n, 1, Length[p]}]; a
%Y Cf. A000043, A000668, A124477, A139484, A145038, A112633, A145041, A145042, A145044, A145045, A145046.
%K nonn
%O 1,1
%A _Artur Jasinski_, Sep 30 2008
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