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 A307865 #13 May 16 2019 03:49:39 %S A307865 0,1,2,3,0,5,6,1,8,9,0,11,0,1,14,15,0,1,18,1,20,21,0,23,0,1,26,1,0,29, %T A307865 30,1,0,33,0,35,36,1,0,39,0,41,4,1,44,9,0,1,48,1,50,51,0,53,54,1,56,1, %U A307865 0,1,0,1,2,63,0,65,0,1,68,69,0,1,0,1,74,75,0,1,78,1,0,81,0,83,0,1,86 %N A307865 a(n) is the number of natural bases b < 2n+1 such that b^n == -1 (mod 2n+1). %C A307865 For n > 0, a(n) = n if and only if 2n+1 is prime. %C A307865 Note that a(n) < n if and only if 2n+1 is composite. %C A307865 Conjecture: if 2n+1 is an absolute Euler pseudoprime, then a(n) = 0. %t A307865 a[n_] := Length[Select[Range[2n], PowerMod[#, n, 2n+1] == 2n &]]; Array[a, 100] (* _Amiram Eldar_, May 02 2019 *) %o A307865 (PARI) a(n) = sum(b=1, 2*n, Mod(b, 2*n+1)^n == -1); \\ _Michel Marcus_, May 02 2019 %Y A307865 Cf. A033181, A053760, A307864. %K A307865 nonn %O A307865 0,3 %A A307865 _Thomas Ordowski_, May 02 2019 %E A307865 More terms from _Amiram Eldar_, May 02 2019