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 A045317 #19 Jun 22 2025 15:23:55
%S A045317 2,3,11,13,23,47,59,71,83,107,109,131,167,179,181,191,227,229,239,251,
%T A045317 263,277,311,313,347,359,383,419,421,431,433,443,467,479,491,503,541,
%U A045317 563,587,599,601,647,659,683,709
%N A045317 Primes p such that x^8 = 3 has a solution mod p.
%C A045317 Complement of A045318 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012
%C A045317 Union of 2, 5, A068231 (primes congruent to 11 modulo 12), prime p == 5 (mod 8) such that 3^((p-1)/4) == 1 (mod p), and primes p == 1 (mod 8) such that 3^((p-1)/8) == 1 (mod p). - _Jianing Song_, Jun 22 2025
%H A045317 Vincenzo Librandi, <a href="/A045317/b045317.txt">Table of n, a(n) for n = 1..1000</a>
%t A045317 ok[p_]:= Reduce[Mod[x^8- 3, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)
%o A045317 (Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^8 eq 3}]; // _Vincenzo Librandi_, Sep 13 2012
%o A045317 (PARI) isok(p) = isprime(p) && ispower(Mod(3, p), 8); \\ _Michel Marcus_, Oct 17 2018
%o A045317 (PARI) isA045317(p) = isprime(p) && (p==2 || p==3 || p%12==11 || (p%8==5 && Mod(3, p)^((p-1)/4) == 1) || (p%8==1 && Mod(3, p)^((p-1)/8) == 1)) \\ _Jianing Song_, Jun 22 2025
%Y A045317 Cf. A000040, A045318.
%Y A045317 A068231 < A385220 < this sequence < A040101 < A097933 (ignoring terms 2, 3), where Ax < Ay means that Ax is a subsequence of Ay.
%K A045317 nonn,easy
%O A045317 1,1
%A A045317 _N. J. A. Sloane_