A042966 Primes p such that x^7 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 199, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 277, 283, 293, 307, 311, 313, 317, 331

Offset

1,1

Comments

Coincides with sequence of "primes p such that x^49 = 2 has a solution mod p" for first 572 terms, then diverges.

Complement of A042967 relative to A000040. - Vincenzo Librandi, Sep 13 2012

a(98) = 631 is the first such prime that is congruent to 1 (mod 7). - Georg Fischer, Jan 06 2022

Links

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

Index entries for related sequences

Mathematica

ok[p_]:= Reduce[Mod[x^7 - 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(400) | exists{x: x in ResidueClassRing(p) | x^7 eq 2}]; // Bruno Berselli, Sep 12 2012

Crossrefs

Cf. A000040, A042967.

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: A161929 A216882 A216881 * A128898 A006514 A216286

Adjacent sequences: A042963 A042964 A042965 * A042967 A042968 A042969

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved