A323576 - OEIS

%I #37 Jul 19 2024 04:30:51

%S 29,197,211,379,421,491,547,659,701,757,827,883,1373,1499,1667,1877,

%T 2213,2269,2339,2437,2549,2843,3011,3067,3347,3557,3571,3613,3851,

%U 3907,4019,4229,4243,4397,4621,4691,4789,4957,5573,5741,5923,6203,6469,6637,6763,6917

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

%C Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) and that p == 1 (mod 7).

%C 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).

%H Amiram Eldar, <a href="/A323576/b323576.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ArtinsConstant.html">Artin's constant</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots">Artin's conjecture on primitive roots</a>.

%o (PARI) forprime(p=3, 7000, if(znorder(Mod(2, p))==(p-1) && p%7==1, print1(p, ", ")))

%Y Cf. A001122, A005596, A000720.

%Y 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).

%K nonn

%O 1,1

%A _Jianing Song_, Aug 30 2019