This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A323590 #19 Feb 16 2025 08:33:57 %S A323590 53,131,443,547,677,859,1171,1301,1483,2029,2237,2549,2861,2939,3797, %T A323590 4603,5227,5851,6397,6709,6917,7229,7307,7411,7541,7853,8243,8269, %U A323590 8867,8971,9283,9491,9803,9907,10037,10141,10427,10973,11779,11909,11987,12611,12637,12923 %N A323590 Primes p such that 2 is a primitive root modulo p while 8192 is not. %C A323590 Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) and that p == 1 (mod 13). %C A323590 According to Artin's conjecture, the number of terms <= N is roughly ((12/155)*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 A323590 Robert Israel, <a href="/A323590/b323590.txt">Table of n, a(n) for n = 1..10000</a> %H A323590 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ArtinsConstant.html">Artin's constant</a> %H A323590 Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots">Artin's conjecture on primitive roots</a> %p A323590 filter:= proc(p) isprime(p) and numtheory:-order(2,p) = p-1 end proc: %p A323590 select(filter, [seq(i, i = 1 .. 13000, 26)]); # _Robert Israel_, Dec 20 2023 %o A323590 (PARI) forprime(p=3, 13000, if(znorder(Mod(2, p))==(p-1) && p%13==1, print1(p, ", "))) %Y A323590 Cf. A001122, A005596, A000720. %Y A323590 Primes p such that 2 is a primitive root modulo p and that p == 1 (mod q): A307627 (q=3), A307628 (q=5), A323576 (q=7), A323577 (q=11), this sequence (q=13). %K A323590 nonn %O A323590 1,1 %A A323590 _Jianing Song_, Aug 30 2019