A323628 Primes p such that 3 is a primitive root modulo p while 2187 is not.

29, 43, 113, 127, 197, 211, 281, 379, 449, 463, 617, 631, 701, 953, 1373, 1709, 1723, 2129, 2143, 2213, 2311, 2381, 2549, 2633, 2647, 2731, 2801, 2969, 3137, 3389, 3557, 3571, 3823, 4159, 4229, 4243, 4327, 4397, 4481, 4649, 4663, 4817, 4831, 4999, 5237, 5419

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 7).

According to Artin's conjecture, the number of terms <= N is roughly ((6/41)*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

select(p -> isprime(p) and numtheory:-order(3, p)=p-1, [seq(i, i=1..10000, 7)]); # Robert Israel, Sep 01 2019

Prog

(PARI) forprime(p=5, 5500, if(znorder(Mod(3, p))==(p-1) && p%7==1, print1(p, ", ")))

Crossrefs

Cf. A019334, A005596, A000720.

Primes p such that 3 is a primitive root modulo p and that p == 1 (mod q): A323594 (q=3), A323617 (q=5), this sequence (q=7).

Sequence in context: A043171 A043951 A042973 * A020997 A108280 A248429

Adjacent sequences: A323625 A323626 A323627 * A323629 A323630 A323631

Keyword

nonn

Author

Jianing Song, Aug 30 2019

Status

approved