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 A045316 #21 Jun 22 2024 22:23:39
%S A045316 3,5,11,13,17,19,29,37,41,43,53,59,61,67,83,97,101,107,109,113,131,
%T A045316 137,139,149,157,163,173,179,181,193,197,211,227,229,241,251,269,277,
%U A045316 281,283,293,307,313,317,331,347,349,353,373,379,389
%N A045316 Primes p such that x^8 = 2 has no solution mod p.
%C A045316 Complement of A045315 relative to A000040. Coincides for the first 140 terms with the sequence of primes p such that x^16 = 2 has no solution mod p (first divergence is at 1217, cf. A059287). - _Klaus Brockhaus_, Jan 26 2001
%C A045316 Differs from A059349 (x^32 == 2 (mod p) has no solution) first at a(37) = A059349(38), the term A059349(37) = 257 which is not in this sequence. See A070184 for all such terms. - _M. F. Hasler_, Jun 21 2024
%H A045316 Vincenzo Librandi, <a href="/A045316/b045316.txt">Table of n, a(n) for n = 1..1000</a>
%t A045316 ok[p_]:= Reduce[Mod[x^8 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 19 2012 *)
%o A045316 (Magma) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^8 eq 2} ]; // _Vincenzo Librandi_, Sep 19 2012
%o A045316 (PARI) select( {is_A045316(p)=Mod(2,p)^(p\gcd(8,p-1))!=1 && p>2}, primes(199)) \\ Append "&& isprime(p)" if that's not known. - _M. F. Hasler_, Jun 22 2024
%Y A045316 Cf. A000040, A045315 (complement in the primes), A059287.
%Y A045316 Subsequence of A059349 (same with x^32), complement is A070184.
%K A045316 nonn,easy
%O A045316 1,1
%A A045316 _N. J. A. Sloane_