login
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.
0
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.
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
KEYWORD
nonn,more
AUTHOR
Luis H. Gallardo, May 05 2022
STATUS
approved