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A323594 Primes p such that 3 is a primitive root modulo p while 27 is not. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..49.

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

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)