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%I #17 Sep 08 2022 08:45:02
%S 3,5,7,11,13,17,19,29,37,41,43,53,59,61,67,73,79,83,97,101,103,107,
%T 109,113,131,137,139,149,151,157,163,173,179,181,193,197,199,211,227,
%U 229,241,251,269,271,277,281,283,293,307,313,317,331,337,347,349,353,367
%N Primes p such that x^24 = 2 has no solution mod p.
%C Complement of A049556 relative to A000040.
%C Coincides for the first 23 terms with sequence A059264 of primes p such that x^12 = 2 has no solution mod p (first divergence is at 113, cf. A059331).
%C Coincides for the first 161 terms with sequence A212376 of primes p such that x^48 = 2 has no solution mod p (first divergence is at 1217, cf. A059669).
%H Bruno Berselli, <a href="/A059362/b059362.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] &] (* _Bruno Berselli_, Sep 14 2012 *)
%t ok[p_] := Reduce[Mod[x^24 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)
%o (Magma) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^24 ne 2}]; // _Bruno Berselli_, Sep 14 2012
%Y Cf. A000040, A049556, A059264, A059331, A059669, A212376.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 27 2001
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