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 A323617 #34 Feb 16 2025 08:33:57 %S A323617 31,101,211,281,331,401,461,521,571,631,641,691,701,751,811,821,881, %T A323617 941,1061,1231,1291,1301,1361,1481,1601,1721,1831,1901,1951,2011,2081, %U A323617 2141,2311,2371,2381,2731,2741,2801,2861,3041,3271,3331,3391,3461,3571,3581,3701,3761,3821,3931 %N A323617 Primes p such that 3 is a primitive root modulo p while 243 is not. %C A323617 Primes p such that 3 is a primitive root modulo p (i.e., p is in A019334) and that p == 1 (mod 5). %C A323617 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 A323617 Amiram Eldar, <a href="/A323617/b323617.txt">Table of n, a(n) for n = 1..10000</a> %H A323617 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ArtinsConstant.html">Artin's constant</a>. %H A323617 Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots">Artin's conjecture on primitive roots</a>. %o A323617 (PARI) forprime(p=5, 4000, if(znorder(Mod(3, p))==(p-1) && p%5==1, print1(p, ", "))) %Y A323617 Cf. A019334, A005596, A000720. %Y A323617 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 A323617 nonn %O A323617 1,1 %A A323617 _Jianing Song_, Aug 30 2019