A040038 Primes p such that x^3 = 3 has no solution mod p.

7, 13, 19, 31, 37, 43, 79, 97, 109, 127, 139, 157, 163, 181, 199, 211, 223, 229, 241, 277, 283, 313, 331, 337, 349, 373, 379, 397, 409, 421, 433, 457, 463, 487, 541, 571, 601, 607, 631, 673, 691, 709, 733, 739

Offset

1,1

Comments

Primes of the form 7x^2+3xy+9y^2, whose discriminant is -243. - T. D. Noe, May 17 2005

Complement of A040036 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

ok[p_]:= Reduce[Mod[x^3 - 3, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 17 2012  *)

Prog

(Magma) [p: p in PrimesUpTo(1000) | not exists{x : x in ResidueClassRing(p) | x^3 eq 3} ]; // Vincenzo Librandi, Sep 17 2012
(PARI) forprime(p=2, 10^3, if(#polrootsmod(x^3-3, p)==0, print1(p, ", "))) \\ Joerg Arndt, Jul 16 2015

Crossrefs

Sequence in context: A040079 A038160 A106870 * A081765 A257002 A216567

Adjacent sequences: A040035 A040036 A040037 * A040039 A040040 A040041

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved