A356856 Primes p such that the least positive primitive root of p (A001918) divides p-1.

2, 3, 5, 7, 11, 13, 19, 29, 31, 37, 43, 53, 59, 61, 67, 71, 79, 83, 101, 107, 109, 127, 131, 139, 149, 151, 163, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 239, 269, 271, 283, 293, 317, 331, 347, 349, 367, 373, 379, 389, 419, 421, 443, 461, 463, 467, 487

Offset: 1

Author

Giorgos Kalogeropoulos, Aug 31 2022

Keywords

• nonn

Comments

If Artin's conjecture is true then this sequence is infinite because it contains all primes with primitive root 2.

Conjecture: This sequence has density ~0.548 in the prime numbers.

Examples

			71 is a term because the least primitive root of the prime number 71 is 7 and 7 divides 71 - 1 = 70.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006093, A001918.

Programs

Maple

filter:= proc(p) local r;
  if not isprime(p) then return false fi;
  r:= NumberTheory:-PrimitiveRoot(p);
  p-1 mod r = 0
end proc:
select(filter, [2,seq(i,i=3..1000,2)]); # Robert Israel, Aug 31 2023

Mathematica

Select[Prime@Range@100, Mod[# - 1, PrimitiveRoot@#] == 0 &]