A377172 - OEIS

%I #23 Nov 13 2024 05:23:26

%S 17,23,37,41,43,47,67,89,109,113,137,139,157,163,167,191,229,233,239,

%T 257,263,277,283,311,349,353,359,379,383,397,421,449,479,503,521,523,

%U 541,547,569,571,593,599,613,619,641,647,661,719,733,739,743,757,761,787,809,811,839,853,857,859,863,877,887,911,929,953,977,983

%N Primes p such that -3/2 is a primitive root modulo p.

%C If p is a term in this sequence, then -3/2 is not a square modulo p (i.e., p is in A191059).

%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(-3/2, 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: this sequence (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).

%Y Cf. A191059, A005596.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Oct 18 2024