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 A376473 #14 Oct 18 2024 17:59:36
%S A376473 951481,2215441,28758601,81844921,1221936841,10370479321,16287076081,
%T A376473 26946809137,33663998161,35094800881,134619011281,188455112353,
%U A376473 299226038833,314240366881,383116075201,594981050401,1230227375833,1572186445201,2096189123113,2377714473001
%N A376473 Numbers k such that 2^(2^(k-1)-1) == 1 (mod k^2) and 2^(k-1) =/= 1 (mod k).
%C A376473 The terms k of A374953 for which A002326((k-1)/2) is odd.
%C A376473 Numbers k in A376253 that are not strong pseudoprimes to base 2.
%C A376473 Every term of this sequence must have a Wieferich prime factor (for example, 951481 = 271 * 3511). The Wieferich prime 1093 cannot divide such a number (see A374953).
%t A376473 q[k_] := Module[{m = MultiplicativeOrder[2, k^2]}, PowerMod[2, k - 1, m] == 1]; Select[Range[1, 2300000, 2], PowerMod[2, # - 1, #] != 1 && q[#] &] (* _Amiram Eldar_, Sep 24 2024 *)
%o A376473 (PARI) is(k) = (k > 1) && k % 2 && !isprime(k) && Mod(2, k)^(k-1) != 1 && Mod(2, znorder(Mod(2, k^2)))^(k-1) == 1; \\ _Amiram Eldar_, Sep 24 2024
%o A376473 (PARI) list(lim)=my(v=List()); if(lim>3<<64, warning("May miss multiples of Wieferich primes > 2^64.")); forstep(n=10533,lim,7022, if(Mod(2, znorder(Mod(2, n^2)))^(n-1) == 1 && Mod(2,n)^n != 2, listput(v,n))); Vec(v) \\ _Charles R Greathouse IV_, Sep 24 2024
%Y A376473 Subsequence of A374953.
%Y A376473 Cf. A001220, A002326, A001262, A001567, A376253.
%K A376473 nonn
%O A376473 1,1
%A A376473 _Thomas Ordowski_, Sep 24 2024
%E A376473 More terms from _Amiram Eldar_, Sep 24 2024