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Primes p such that -9/2 is a primitive root modulo p.
6

%I #8 Oct 23 2024 20:26:43

%S 5,13,23,29,31,47,53,61,71,79,101,109,149,151,157,167,173,191,197,199,

%T 223,229,239,263,269,277,293,311,317,359,367,373,383,389,461,463,479,

%U 487,503,509,557,599,613,647,653,661,677,701,709,719,733,743,757,773,797,821,823,829,839,853,863,887,911,967,983,991

%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 A003628).

%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), A377178 (a=9).

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

%Y Cf. A003628, A005596.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Oct 18 2024