A040084 - OEIS

%I #12 Sep 08 2022 08:44:53

%S 7,13,31,37,43,61,67,73,79,103,139,157,163,193,199,211,223,229,241,

%T 331,337,349,367,379,397,433,439,457,463,499,523,541,547,571,601,607,

%U 619,631,643,673,709,727,739,751

%N Primes p such that x^3 = 19 has no solution mod p.

%C Complement of A040083 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040084/b040084.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[200]], ok] (* _Vincenzo Librandi_, Sep 17 2012  *)

%o (Magma) [p: p in PrimesUpTo(1000) | not exists{x : x in ResidueClassRing(p) | x^3 eq 19} ]; // _Vincenzo Librandi_, Sep 17 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.