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A323590 Primes p such that 2 is a primitive root modulo p while 8192 is not. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..44.

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

Wikipedia, Artin's conjecture on primitive roots

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

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Last modified January 28 13:57 EST 2023. Contains 359894 sequences. (Running on oeis4.)