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A059257
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Primes p such that x^47 = 2 has no solution mod p.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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ok[p_]:= Reduce[Mod[x^47 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[1800]], ok] (* Vincenzo Librandi, Sep 20 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A000040, A058853.
Sequence in context: A142699 A113157 A142446 * A332676 A142837 A064964
Adjacent sequences: A059254 A059255 A059256 * A059258 A059259 A059260
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KEYWORD
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nonn,easy
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AUTHOR
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Klaus Brockhaus, Jan 23 2001
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STATUS
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approved
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