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 A059245 Primes p such that x^13 = 2 has no solution mod p. 10
 53, 79, 131, 157, 313, 443, 521, 547, 599, 677, 859, 911, 937, 1093, 1171, 1223, 1249, 1301, 1327, 1483, 1613, 1847, 1873, 1951, 2003, 2029, 2081, 2237, 2341, 2393, 2549, 2731, 2861, 2887, 2939, 3121, 3251, 3329, 3407, 3433, 3511, 3719, 3797, 3823, 4057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Complement of A049545 relative to A000040. Presumably this is the same as Primes congruent to 1 mod 13. - N. J. A. Sloane, Jul 11 2008 The smallest counterexample is 4421: 4421 == 1 (mod 13), but 162^13 == 2 (mod 4421), therefore this prime is not in the sequence. - Bruno Berselli, Sep 12 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 MATHEMATICA Select[Prime[Range[PrimePi[5000]]], ! MemberQ[PowerMod[Range[#], 13, #], Mod[2, #]] &] (* T. D. Noe, Sep 12 2012 *) ok[p_]:= Reduce[Mod[x^13 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[600]], ok] (* Vincenzo Librandi, Sep 20 2012  *) PROG (MAGMA) [p: p in PrimesUpTo(4500) | forall{x: x in ResidueClassRing(p) | x^13 ne 2}]; // Bruno Berselli, Sep 12 2012 CROSSREFS Cf. A000040, A049545. Sequence in context: A032421 A129257 A125875 * A268753 A125876 A136065 Adjacent sequences:  A059242 A059243 A059244 * A059246 A059247 A059248 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Jan 21 2001 STATUS approved

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Last modified August 24 03:20 EDT 2019. Contains 326260 sequences. (Running on oeis4.)