A351688 Prime numbers p such that the order of the (p-1)-th Bell number B(p-1) is a power of 2 modulo p.

3, 17, 23, 37, 67, 89, 193, 227, 257, 593, 641, 769, 1889, 10331, 12289, 13441, 18433, 40961, 65537, 85121, 96769, 2752513, 3655681

Offset: 1

Author

Luis H. Gallardo, May 05 2022

Keywords

• nonn
• more

Comments

An odd prime p is a counterexample of Kurepa's conjecture if and only if B(p-1) = 1 modulo p.

Examples

			a(1)=3 since B(2)=2 has order 2 modulo 3.
a(3)=37, since B(36)=6 modulo 37 has order 4 = 2^2 modulo 37.
		

Crossrefs

Cf. A000110.

Programs

Mathematica

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 *)