A323576 Primes p such that 2 is a primitive root modulo p while 128 is not.

29, 197, 211, 379, 421, 491, 547, 659, 701, 757, 827, 883, 1373, 1499, 1667, 1877, 2213, 2269, 2339, 2437, 2549, 2843, 3011, 3067, 3347, 3557, 3571, 3613, 3851, 3907, 4019, 4229, 4243, 4397, 4621, 4691, 4789, 4957, 5573, 5741, 5923, 6203, 6469, 6637, 6763, 6917

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 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

Table of n, a(n) for n=1..46.

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

Wikipedia, Artin's conjecture on primitive roots

Prog

(PARI) forprime(p=3, 7000, if(znorder(Mod(2, p))==(p-1) && p%7==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), this sequence (q=7), A323577 (q=11), A323590 (q=13).

Sequence in context: A126497 A087767 A142226 * A142653 A237446 A144731

Adjacent sequences: A323573 A323574 A323575 * A323577 A323578 A323579

Keyword

nonn

Author

Jianing Song, Aug 30 2019

Status

approved