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

1,1

Comments

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

Links

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

Example

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

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

Crossrefs

Cf. A000110, A005596, A350429.

Sequence in context: A378271 A082618 A020610 * A257529 A030482 A019366

Adjacent sequences: A351679 A351680 A351681 * A351683 A351684 A351685

Keyword

nonn

Author

Luis H. Gallardo, May 04 2022

Extensions

Corrected by Robert Israel, May 04 2023

Status

approved