A307865 - OEIS

%I #13 May 16 2019 03:49:39

%S 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 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 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 a(n) is the number of natural bases b < 2n+1 such that b^n == -1 (mod 2n+1).

%C For n > 0, a(n) = n if and only if 2n+1 is prime.

%C Note that a(n) < n if and only if 2n+1 is composite.

%C Conjecture: if 2n+1 is an absolute Euler pseudoprime, then a(n) = 0.

%t a[n_] := Length[Select[Range[2n], PowerMod[#, n, 2n+1] == 2n &]]; Array[a, 100] (* _Amiram Eldar_, May 02 2019 *)

%o (PARI) a(n) = sum(b=1, 2*n, Mod(b, 2*n+1)^n == -1); \\ _Michel Marcus_, May 02 2019

%Y Cf. A033181, A053760, A307864.

%K nonn

%O 0,3

%A _Thomas Ordowski_, May 02 2019

%E More terms from _Amiram Eldar_, May 02 2019