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 A374953 #14 Jul 25 2024 11:05:48
%S A374953 66709,951481,2215441,2847421,4111381,4869757,28758601,81844921,
%T A374953 124187581,300510001,306197821,1221936841,9763146541,10370479321,
%U A374953 13560714361,14387344201,16287076081,16956342901,18820810297,19245374461,22732640101,26946809137,27119213281,29217386881
%N A374953 Numbers k such that 2^(2^k-2) == 1 (mod k^2) and 2^(k-1) =/= 1 (mod k).
%C A374953 The composite terms of A374841 that are not in A001567.
%C A374953 Every term of this sequence must have a Wieferich prime factor (for example 66709 = 19 * 3511). Wieferich prime p = 1093 cannot divide such k, since it would require ord_{p^2}(2) = 364 = 2^2 * 91 to divide 2^k - 2, which is impossible. - _Max Alekseyev_, Jul 25 2024
%t A374953 f[n_] := Module[{e = IntegerExponent[n^2, 2], d, k, r}, d = n^2 / 2^e; k = MultiplicativeOrder[2, d]; r = PowerMod[2, n, k] - e - 2; r = Mod[r, k]; 2^e * PowerMod[2, r, d]];
%t A374953 q[n_] := PowerMod[2, n-1, n] != 1 && f[n] == 1;
%t A374953 Select[Range[10^6], CompositeQ[#] && q[#] &] (* or: *)
%t A374953 Select[3511 * Range[10^5], q] (* faster, can be used for generating terms up to 4.97*10^17, the current lower bound for A001220(3) *)
%t A374953 (* _Amiram Eldar_, Jul 25 2024 after _T. D. Noe_ at A155836 *)
%Y A374953 Cf. A001220, A001567, A374841, A001567.
%K A374953 nonn
%O A374953 1,1
%A A374953 _Thomas Ordowski_, Jul 25 2024
%E A374953 More terms from _Amiram Eldar_, Jul 25 2024