A323590 Primes p such that 2 is a primitive root modulo p while 8192 is not.

53, 131, 443, 547, 677, 859, 1171, 1301, 1483, 2029, 2237, 2549, 2861, 2939, 3797, 4603, 5227, 5851, 6397, 6709, 6917, 7229, 7307, 7411, 7541, 7853, 8243, 8269, 8867, 8971, 9283, 9491, 9803, 9907, 10037, 10141, 10427, 10973, 11779, 11909, 11987, 12611, 12637, 12923

Offset

1,1

Comments

Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) and that p == 1 (mod 13).

According to Artin's conjecture, the number of terms <= N is roughly ((12/155)*C)*PrimePi(N), where C is the Artin's constant = A005596, PrimePi = A000720. Compare: the number of terms of A001122 that are no greater than N is roughly C*PrimePi(N).

Links

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

Eric Weisstein's World of Mathematics, Artin's constant

Wikipedia, Artin's conjecture on primitive roots

Maple

filter:= proc(p) isprime(p) and numtheory:-order(2, p) = p-1 end proc:
select(filter, [seq(i, i = 1 .. 13000, 26)]); # Robert Israel, Dec 20 2023

Prog

(PARI) forprime(p=3, 13000, if(znorder(Mod(2, p))==(p-1) && p%13==1, print1(p, ", ")))

Crossrefs

Cf. A001122, A005596, A000720.

Primes p such that 2 is a primitive root modulo p and that p == 1 (mod q): A307627 (q=3), A307628 (q=5), A323576 (q=7), A323577 (q=11), this sequence (q=13).

Sequence in context: A177105 A246933 A142167 * A044304 A044685 A239721

Adjacent sequences: A323587 A323588 A323589 * A323591 A323592 A323593

Keyword

nonn

Author

Jianing Song, Aug 30 2019

Status

approved