A051078 - OEIS

%I #21 Sep 08 2022 08:44:59

%S 2,3,11,17,41,43,59,83,89,107,113,131,137,179,227,233,251,257,281,283,

%T 347,353,401,419,443,449,457,467,491,499,521,563,569,587,593,601,617,

%U 641,643,659,683,691,761,809,827,857,881,929,947,953,971,977,1019,1049,1051,1091,1097,1163,1187,1193,1217,1259,1283,1289,1307,1361,1409

%N Primes p such that x^18 = -2 has a solution mod p.

%C Differs from A051096 first at the 640th entry, at p=17659, next at p=23059. - _R. J. Mathar_, Oct 14 2008

%C Complement of A216740 relative to A000040. - _Vincenzo Librandi_, Sep 16 2012

%H Vincenzo Librandi, <a href="/A051078/b051078.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^18 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)

%o (PARI) /* see A051071 */

%o (Magma) [p: p in PrimesUpTo(1410) | exists(t){x : x in ResidueClassRing(p) | x^18 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