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

1,1

Comments

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

Links

Table of n, a(n) for n=1..23.

Example

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.

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 *)

Crossrefs

Cf. A000110.

Sequence in context: A273407 A267067 A322490 * A206626 A128107 A154620

Adjacent sequences: A351685 A351686 A351687 * A351689 A351690 A351691

Keyword

nonn,more

Author

Luis H. Gallardo, May 05 2022

Status

approved