A323628 - OEIS

%I #19 Sep 01 2019 22:06:49

%S 29,43,113,127,197,211,281,379,449,463,617,631,701,953,1373,1709,1723,

%T 2129,2143,2213,2311,2381,2549,2633,2647,2731,2801,2969,3137,3389,

%U 3557,3571,3823,4159,4229,4243,4327,4397,4481,4649,4663,4817,4831,4999,5237,5419

%N Primes p such that 3 is a primitive root modulo p while 2187 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 7).

%C According to Artin's conjecture, the number of terms <= N is roughly ((6/41)*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 Robert Israel, <a href="/A323628/b323628.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>

%p select(p -> isprime(p) and numtheory:-order(3,p)=p-1, [seq(i,i=1..10000,7)]); # _Robert Israel_, Sep 01 2019

%o (PARI) forprime(p=5, 5500, if(znorder(Mod(3, p))==(p-1) && p%7==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), A323617 (q=5), this sequence (q=7).

%K nonn

%O 1,1

%A _Jianing Song_, Aug 30 2019