A059257 Primes p such that x^47 = 2 has no solution mod p.

283, 659, 941, 1129, 1223, 1693, 1787, 2069, 2351, 2539, 2633, 3761, 4231, 4513, 4889, 5077, 5171, 5641, 5923, 6299, 6581, 6863, 7333, 8179, 8273, 8461, 8837, 9871, 10247, 10529, 11093, 11657, 11939, 12409, 12503, 12973, 13537, 13913, 14759

Offset

1,1

Comments

Presumably this is also Primes congruent to 1 mod 47. - N. J. A. Sloane, Jul 11 2008. Not so! The smallest counterexample is 26227: 26227 == 1 (mod 47), but 131^47 == 2 (mod 26227), therefore this prime is not in the sequence. - Bruno Berselli, Sep 12 2012

All terms are 1 mod 94. - Charles R Greathouse IV, Sep 13 2012

Complement of A216885 relative to A000040. - Vincenzo Librandi, Sep 20 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

ok[p_]:= Reduce[Mod[x^47 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[1800]], ok] (* Vincenzo Librandi, Sep 20 2012  *)

Prog

(Magma) [p: p in PrimesUpTo(15000) | forall{x: x in ResidueClassRing(p) | x^47 ne 2}]; // Bruno Berselli, Sep 12 2012
(PARI) select(p->!ispower(Mod(2, p), 47), primes(3000)) \\ Charles R Greathouse IV, Sep 13 2012

Crossrefs

Cf. A000040, A058853.

Sequence in context: A113157 A142446 A345905 * A332676 A142837 A064964

Adjacent sequences: A059254 A059255 A059256 * A059258 A059259 A059260

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 23 2001

Status

approved