%I #34 Feb 16 2025 08:33:57
%S 31,101,211,281,331,401,461,521,571,631,641,691,701,751,811,821,881,
%T 941,1061,1231,1291,1301,1361,1481,1601,1721,1831,1901,1951,2011,2081,
%U 2141,2311,2371,2381,2731,2741,2801,2861,3041,3271,3331,3391,3461,3571,3581,3701,3761,3821,3931
%N Primes p such that 3 is a primitive root modulo p while 243 is not.
%C Primes p such that 3 is a primitive root modulo p (i.e., p is in A019334) and that p == 1 (mod 5).
%C According to Artin's conjecture, the number of terms <= N is roughly ((4/19)*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="/A323617/b323617.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://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=5, 4000, if(znorder(Mod(3, p))==(p-1) && p%5==1, print1(p, ", ")))
%Y Cf. A019334, A005596, A000720.
%Y Primes p such that 3 is a primitive root modulo p and that p == 1 (mod q): A323594 (q=3), this sequence (q=5), A323628 (q=7).
%K nonn,changed
%O 1,1
%A _Jianing Song_, Aug 30 2019