A323594 - OEIS

A323594

Primes p such that 3 is a primitive root modulo p while 27 is not.

7, 19, 31, 43, 79, 127, 139, 163, 199, 211, 223, 283, 331, 379, 463, 487, 571, 607, 631, 691, 739, 751, 811, 823, 859, 907, 1039, 1063, 1087, 1123, 1231, 1279, 1291, 1327, 1423, 1447, 1459, 1483, 1567, 1579, 1627, 1663, 1699, 1723, 1747, 1831, 1951, 1987, 1999

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OFFSET

1,1

COMMENTS

Primes p such that 3 is a primitive root modulo p (i.e., p is in A019334) and that p == 1 (mod 3).

According to Artin's conjecture, the number of terms <= N is roughly ((2/5)*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

Amiram Eldar, 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.

PROG

(PARI) forprime(p=5, 2000, if(znorder(Mod(3, p))==(p-1) && p%3==1, print1(p, ", ")))

CROSSREFS

Complement of A019353 with respect to A019334.

Cf. also A005596, A000720.

Primes p such that 3 is a primitive root modulo p and that p == 1 (mod q): this sequence (q=3), A323617 (q=5), A323628 (q=7).

Sequence in context: A017605 A126194 A068229 * A071696 A216530 A114564

Adjacent sequences: A323591 A323592 A323593 * A323595 A323596 A323597

KEYWORD

nonn

AUTHOR

Jianing Song, Aug 30 2019

STATUS

approved