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A042966 Primes p such that x^7 = 2 has a solution mod p. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes congruent to {0, 2, 3, 4, 5, 6} mod 7.

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

LINKS

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

Index entries for related sequences

MATHEMATICA

Select[Prime[Range[120]], MemberQ[{0, 2, 3, 4, 5, 6}, Mod[#, 7]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2012 *)

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

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Last modified February 17 18:13 EST 2020. Contains 332005 sequences. (Running on oeis4.)