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A040038 Primes p such that x^3 = 3 has no solution mod p. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 08:23 EDT 2018. Contains 315270 sequences. (Running on oeis4.)