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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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, ...

Programs

Magma

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

Mathematica

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