A351682 Prime numbers p such that the (p-1)-st Bell number B(p-1) is a primitive root modulo p.

2, 3, 11, 13, 17, 19, 29, 31, 47, 53, 71, 103, 113, 127, 131, 137, 139, 149, 173, 179, 181, 191, 211, 233, 239, 241, 251, 257, 263, 269, 293, 317, 347, 367, 379, 401, 431, 439, 449, 461, 503, 509, 523, 541, 557, 587, 607, 617, 619, 647, 653, 683, 691, 733, 743, 761, 773, 797, 821, 823, 827, 853, 859, 881, 919, 929

Offset: 1

Author

Luis H. Gallardo, May 04 2022

Keywords

• nonn

Comments

Heuristically, the density of the sequence in the primes should approach Artin's constant: 0.3739558136...

Examples

			For n = 2 one has a(2) = 3 since B(2) = 2 is a primitive root modulo 3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000110, A005596, A350429.

Programs

Maple

filter:= proc(p) local b;
  b:= combinat:-bell(p-1);
  numtheory:-order(b,p) = p-1
end proc:
select(filter, [seq(ithprime(i),i=1..200)]); # Robert Israel, May 04 2023

Extensions

Corrected by Robert Israel, May 04 2023