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A042967
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Primes p such that x^7 = 2 has no solution mod p.
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4
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29, 43, 71, 113, 127, 197, 211, 239, 281, 337, 379, 421, 449, 463, 491, 547, 617, 659, 701, 743, 757, 827, 883, 911, 967, 1009, 1051, 1093, 1289, 1303, 1373, 1429, 1471, 1499, 1583, 1597, 1667, 1723, 1877, 1933, 2017, 2087, 2129, 2213, 2269, 2297, 2311, 2339, 2381, 2423, 2437, 2521
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OFFSET
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1,1
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COMMENTS
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Complement of A042966 relative to A000040. Coincides for the first 96 terms with the sequence of primes p such that x^49 = 2 has no solution mod p (first divergence is at 4999, cf. A059667) - Klaus Brockhaus, Feb 04 2001
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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^7 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[700]], ok] (* Vincenzo Librandi, Sep 19 2012 *)
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PROG
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(MAGMA) [p: p in PrimesUpTo(3000) | forall{x: x in ResidueClassRing(p) | x^7 ne 2}]; // Vincenzo Librandi, Aug 21 2012
(MAGMA) [p: p in PrimesUpTo(2600) | not exists{x : x in ResidueClassRing(p) | x^7 eq 2} ]; // Vincenzo Librandi, Sep 19 2012
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CROSSREFS
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Cf. A000040, A042966, A059667.
Sequence in context: A004619 A140444 A042969 * A061638 A136062 A039348
Adjacent sequences: A042964 A042965 A042966 * A042968 A042969 A042970
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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