A323577 Primes p such that 2 is a primitive root modulo p while 2048 is not.

67, 419, 661, 859, 947, 1123, 1277, 1453, 2069, 2267, 2333, 2531, 2707, 2861, 3037, 3323, 3499, 3851, 3917, 4093, 4357, 4621, 4973, 5171, 5501, 6029, 6469, 6491, 6733, 7019, 7283, 7349, 7459, 7547, 7789, 7877, 8053, 8669, 8867, 8933, 9901, 9923, 10099, 10253, 10891, 10979

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 11).

According to Artin's conjecture, the number of terms <= N is roughly ((10/109)*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, 12000, if(znorder(Mod(2, p))==(p-1) && p%11==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), this sequence (q=11), A323590 (q=13).

Sequence in context: A142371 A142609 A262344 * A142735 A342803 A219736

Adjacent sequences: A323574 A323575 A323576 * A323578 A323579 A323580

Keyword

nonn

Author

Jianing Song, Aug 30 2019

Status

approved