A059245 Primes p such that x^13 = 2 has no solution mod p.

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

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, A268753.

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