A216885 -id:A216885 - cp's OEIS frontend

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

Klaus Brockhaus, Jan 23 2001

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

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

Cf. A000040, A058853.

[p: p in PrimesUpTo(15000) | forall{x: x in ResidueClassRing(p) | x^47 ne 2}]; // Bruno Berselli, Sep 12 2012

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

select(p->!ispower(Mod(2,p),47),primes(3000)) \\ Charles R Greathouse IV, Sep 13 2012

cp's OEIS Frontend

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

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