|
%I #25 May 08 2022 08:23:08
%S 3,17,23,37,67,89,193,227,257,593,641,769,1889,10331,12289,13441,
%T 18433,40961,65537,85121,96769,2752513,3655681
%N Prime numbers p such that the order of the (p-1)-th Bell number B(p-1) is a power of 2 modulo p.
%C An odd prime p is a counterexample of Kurepa's conjecture if and only if B(p-1) = 1 modulo p.
%e a(1)=3 since B(2)=2 has order 2 modulo 3.
%e a(3)=37, since B(36)=6 modulo 37 has order 4 = 2^2 modulo 37.
%t Do[p = Prime[k]; m = Mod[BellB[p-1], p]; If[m != 0, f = FactorInteger[MultiplicativeOrder[m, p]]; If[Length[f] == 1 && f[[1, 1]] == 2, Print[p]]], {k, 1, 500}] (* _Vaclav Kotesovec_, May 06 2022 *)
%Y Cf. A000110.
%K nonn,more
%O 1,1
%A _Luis H. Gallardo_, May 05 2022
|
