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%I #19 Sep 08 2022 08:44:53
%S 7,13,19,31,37,43,79,97,109,127,139,157,163,181,199,211,223,229,241,
%T 277,283,313,331,337,349,373,379,397,409,421,433,457,463,487,541,571,
%U 601,607,631,673,691,709,733,739
%N Primes p such that x^3 = 3 has no solution mod p.
%C Primes of the form 7x^2+3xy+9y^2, whose discriminant is -243. - _T. D. Noe_, May 17 2005
%C Complement of A040036 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012
%H Vincenzo Librandi, <a href="/A040038/b040038.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_]:= Reduce[Mod[x^3 - 3, 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 3} ]; // _Vincenzo Librandi_, Sep 17 2012
%o (PARI) forprime(p=2,10^3,if(#polrootsmod(x^3-3,p)==0,print1(p,", "))) \\ _Joerg Arndt_, Jul 16 2015
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_.
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