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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

Magma

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

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 *)

Extensions

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