A323577 - OEIS

%I #42 Jul 19 2024 08:46:11

%S 67,419,661,859,947,1123,1277,1453,2069,2267,2333,2531,2707,2861,3037,

%T 3323,3499,3851,3917,4093,4357,4621,4973,5171,5501,6029,6469,6491,

%U 6733,7019,7283,7349,7459,7547,7789,7877,8053,8669,8867,8933,9901,9923,10099,10253,10891,10979

%N Primes p such that 2 is a primitive root modulo p while 2048 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 11).

%C 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).

%H Amiram Eldar, <a href="/A323577/b323577.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, 12000, if(znorder(Mod(2, p))==(p-1) && p%11==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), A323576 (q=7), this sequence (q=11), A323590 (q=13).

%K nonn

%O 1,1

%A _Jianing Song_, Aug 30 2019