A040993 Primes p such that x^6 = 2 has no solution mod p.

3, 5, 7, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 349, 367, 373, 379, 389, 397, 409

Offset

1,1

Comments

Complement of A040992 relative to A000040. Coincides for the first 58 terms with A212375, that is the sequence of primes p such that x^18 = 2 has no solution mod p (first divergence is at 433, cf. A059664). Also coincides for the first 58 terms with sequence of primes p such that x^54 = 2 has no solution mod p (first divergence is at 433, cf. A059665). The sequence for x^18 and the sequence for x^54 coincide for the first 379 terms (first divergence is at 3943, cf. A059666). - Klaus Brockhaus, Feb 04 2001

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Mathematica

Select[Prime[Range[PrimePi[500]]], ! MemberQ[PowerMod[Range[#], 6, #], Mod[2, #]] &] (* Bruno Berselli, Sep 13 2012 *)
ok[p_] := Reduce[Mod[x^6 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^6 ne 2}]; // Bruno Berselli, Sep 13 2012

Crossrefs

Cf. A000040, A040992, A049550, A059664, A059665, A059666, A212375.

Sequence in context: A290817 A059353 A212375 * A078425 A020587 A249077

Adjacent sequences: A040990 A040991 A040992 * A040994 A040995 A040996

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

A212375 added in the Brockhaus comment from Bruno Berselli, Sep 13 2012

Status

approved