%I #18 Sep 08 2022 08:44:59
%S 2,3,11,19,43,59,67,73,83,89,107,113,131,139,163,179,211,227,233,251,
%T 257,281,283,307,331,337,347,353,379,419,443,467,491,499,523,547,563,
%U 571,577,587,593,601,617,619,643,659,683,691,739,787,811,827,859,881,883,907,937,947,971,1019,1033,1049,1051,1091,1097,1123
%N Primes p such that x^4 = -2 has a solution mod p.
%C Complement of A216690 relative to A000040. - _Vincenzo Librandi_, Sep 16 2012
%H Vincenzo Librandi, <a href="/A051071/b051071.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_]:= Reduce[Mod[x^4 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)
%o (PARI)
%o forprime(p=2,2000,if([]~!=polrootsff(x^4+2,p,y-1),print1(p,", ")));print();
%o /* or: */
%o forprime(p=2,2000,if([]~!=polrootsmod(x^4+2,p),print1(p,", ")));print();
%o /* faster */ /* _Joerg Arndt_, Jul 27 2011 */
%o (Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^4 eq - 2}]; // _Vincenzo Librandi_, Sep 15 2012
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Joerg Arndt_, Jul 27 2011