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 A322121 #21 Jan 27 2019 09:26:27 %S A322121 25,49,65,85,91,121,125,133,145,169,185,205,217,221,247,259,265,289, %T A322121 301,305,325,341,343,361,365,377,403,425,427,445,451,469,481,485,493, %U A322121 505,511,529,533,545,553,559,565,589,625,629,637,671,679,685,689,697,703 %N A322121 Composite numbers m such that b^(m-1) == 1 (mod (b^2-1)*m) has a solution b. %C A322121 The smallest solutions b are 7, 18, 8, 13, 3, 3, 57, 11, ... %C A322121 These numbers m are odd and indivisible by 3. %C A322121 They contain all prime powers p^k for p > 3 and k > 1. %C A322121 It seems that, for a fixed integer k > 0, these are composite numbers m such that c^(m-1) == 1 (mod (c^2-1)m^k) for some base c. %C A322121 Conjecture: If m is a composite number such that b^(m-1) == 1 (mod (b^2-1)m) for some base b, then m is a strong pseudoprime to some base a in the range 2 <= a <= m-2. Thus, these numbers m are probably a proper subset of A181782. %t A322121 aQ[n_] := CompositeQ[n] && LengthWhile[Range[2,n], !Divisible[#^(n-1)-1, (#^2-1) n] &] != n-1; Select[Range[1000],aQ] (* _Amiram Eldar_, Nov 27 2018 *) %Y A322121 Cf. A181782, A322120. %K A322121 nonn %O A322121 1,1 %A A322121 _Thomas Ordowski_, Nov 27 2018 %E A322121 More terms from _Amiram Eldar_, Nov 27 2018