A051080 - OEIS

%I #18 Sep 08 2022 08:44:59

%S 2,3,11,17,19,41,43,59,73,83,97,107,113,131,137,139,163,179,193,211,

%T 227,233,241,251,257,281,283,307,313,331,337,347,379,401,409,433,443,

%U 449,457,467,491,499,521,523,547,563,569,571,577,587,593,601,619,641,643,659,673,691,739,761,769,787,809,811,827,857,883,907,929,937,953,971,977,1009

%N Primes p such that x^22 = -2 has a solution mod p.

%C Complement of A216742 relative to A000040. - _Vincenzo Librandi_, Sep 16 2012

%H Vincenzo Librandi, <a href="/A051080/b051080.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[300]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)

%o (PARI) /* see A051071 */

%o (Magma) [p: p in PrimesUpTo(1010) | exists(t){x : x in ResidueClassRing(p) | x^22 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