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A059257 Primes p such that x^47 = 2 has no solution mod p. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A142699 A113157 A142446 * A332676 A142837 A064964

Adjacent sequences:  A059254 A059255 A059256 * A059258 A059259 A059260

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 23 2001

STATUS

approved

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Last modified April 14 05:17 EDT 2021. Contains 342942 sequences. (Running on oeis4.)