%I #13 Sep 08 2022 08:44:53
%S 2,3,5,11,17,19,23,29,41,47,53,59,71,83,89,97,101,107,109,113,127,131,
%T 137,149,151,167,173,179,181,191,197,227,233,239,251,257,263,269,271,
%U 277,281,283,293,307,311,313,317
%N Primes p such that x^3 = 19 has a solution mod p.
%C Complement of A040084 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012
%H Vincenzo Librandi, <a href="/A040083/b040083.txt">Table of n, a(n) for n = 1..1000</a>
%t ok [p_]:=Reduce[Mod[x^3 - 19, p] == 0, x, Integers] =!= False; Select[Prime[Range[180]], ok] (* _Vincenzo Librandi_, Sep 11 2012 *)
%o (Magma) [p: p in PrimesUpTo(450) | exists(t){x : x in ResidueClassRing(p) | x^3 eq 19}]; // _Vincenzo Librandi_, Sep 11 2012
%Y Cf. A000040, A040084.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_.