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%I #10 Mar 19 2023 13:32:46
%S 5,7,13,23,29,31,37,47,53,61,67,71,79,89,101,103,109,127,149,151,157,
%T 167,173,181,191,197,199,223,229,239,263,269,271,277,293,311,317,349,
%U 353,359,367,373,383,389,397,419,421,431,439,461,463,479,487,503,509,541
%N Primes p such that x^22 = -2 has no solution mod p.
%C Complement of A051080 relative to A000040.
%H Vincenzo Librandi, <a href="/A216742/b216742.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_] := Reduce[Mod[x^22 + 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok]
%o (Magma) [p: p in PrimesUpTo(600) | forall{x: x in ResidueClassRing(p) | x^22 ne -2}]; // _Bruno Berselli_, Sep 20 2012
%o (PARI) select(x->!ispower(Mod(-2, x), 22), primes(100)) \\ _Michel Marcus_, Mar 19 2023
%Y Cf. A000040, A051080.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Sep 15 2012
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