A040992 Primes p such that x^6 = 2 has a solution mod p.

2, 17, 23, 31, 41, 47, 71, 89, 113, 127, 137, 167, 191, 223, 233, 239, 257, 263, 281, 311, 353, 359, 383, 401, 431, 433, 439, 449, 457, 479, 503, 521, 569, 593, 599, 601, 617, 641, 647, 719, 727, 743, 761, 809, 839, 857, 863, 881, 887, 911, 919, 929, 953

Offset

1,1

Comments

Complement of A040993 relative to A000040. - Vincenzo Librandi, Sep 13 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Mathematica

ok[p_]:= Reduce[Mod[x^6- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

Prog

(PARI) forprime(p=2, 2000, if([]~!=polrootsmod(x^6-2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jul 27 2011 */
(Magma) [p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^6 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A040993.

For primes p such that x^m == 2 (mod p) has a solution for m = 2,3,4,5,6,7,... see A038873, A040028, A040098, A040159, A040992, A042966, ...

Sequence in context: A332094 A126961 A106622 * A049550 A049574 A018643

Adjacent sequences: A040989 A040990 A040991 * A040993 A040994 A040995

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved