A377178 - OEIS

%I #8 Oct 23 2024 20:26:48

%S 5,13,19,29,43,53,59,61,83,101,107,109,149,157,173,179,197,227,229,

%T 251,269,277,283,293,317,331,347,373,389,419,443,461,467,491,509,523,

%U 547,557,563,587,613,619,653,661,677,683,691,701,709,733,739,757,773,787,797,821,829,853,883,907,947,971

%N Primes p such that 9/2 is a primitive root modulo p.

%C If p is a term in this sequence, then 9/2 is not a square modulo p (i.e., p is in A003629).

%C Conjecture: this sequence has relative density equal to Artin's constant (A005596) with respect to the set of primes.

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

%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>

%o (PARI) forprime(p=5, 10^3, if(znorder(Mod(9/2, p))==p-1, print1(p, ", ")));

%Y Primes p such that +a/2 is a primitive root modulo p: A320384 (a=3), A377174 (a=5), A377176 (a=7), this sequence (a=9).

%Y Primes p such that -a/2 is a primitive root modulo p: A377172 (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).

%Y Cf. A003629, A005596.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Oct 18 2024