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A051101 Primes p such that x^64 = -2 has a solution mod p.

%I A051101 #24 Sep 08 2022 08:44:59
%S A051101 2,3,11,19,43,59,67,83,107,131,139,163,179,211,227,251,281,283,307,
%T A051101 331,347,379,419,443,467,491,499,523,547,563,571,587,617,619,643,659,
%U A051101 683,691,739,787,811,827,859,883,907,947,971,1019,1033,1049,1051,1091,1097,1123,1163,1171,1187
%N A051101 Primes p such that x^64 = -2 has a solution mod p.
%C A051101 Differs from A051085 first at the 541st entry, at p=15809. - _R. J. Mathar_, Oct 14 2008
%C A051101 From _Christopher J. Smyth_, Jul 24 2009: (Start)
%C A051101 Differs from A163183 (primes dividing 2^j+1 for some odd j) at the 827th entry, at p=25601. See comment at A163186 for explanation.
%C A051101 Sequence is union of A163183 and A163186 (primes p such that the equation x^64 = -2 mod p has a solution, and ord_p(-2) is even).
%C A051101 (End)
%C A051101 Complement of A216777 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012
%H A051101 T. D. Noe, <a href="/A051101/b051101.txt">Table of n, a(n) for n = 1..1000</a>
%t A051101 ok[p_]:= Reduce[Mod[x^64 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* _Vincenzo Librandi_, Sep 16 2012 *)
%o A051101 (PARI)
%o A051101 forprime(p=2, 2000, if([]~!=polrootsmod(x^64+2, p), print1(p, ", "))); print();
%o A051101 /* _Joerg Arndt_, Jun 24 2012 */
%o A051101 (Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^64 eq - 2}]; // _Vincenzo Librandi_, Sep 16 2012
%K A051101 nonn,easy
%O A051101 1,1
%A A051101 _N. J. A. Sloane_
%E A051101 More terms from _Joerg Arndt_, Jul 27 2011