A059230 Primes p such that x^61 = 2 has no solution mod p.

367, 733, 977, 1709, 1831, 2441, 3539, 4027, 4271, 4637, 4759, 5003, 5857, 6101, 6833, 7321, 7687, 8053, 8297, 8419, 8663, 9029, 9151, 9883, 10859, 12323, 12689, 13177, 13421, 14153, 14519, 15373, 15739, 16349, 17203, 17569, 18301, 18911

Offset

1,1

Comments

Presumably this is also Primes congruent to 1 mod 61 (A212378). - N. J. A. Sloane, Jul 11 2008

Complement of A216884 relative to A000040. - Vincenzo Librandi, Sep 20 2012

Regarding the first comment, the smallest counterexample is the prime 34039: 34039 == 1 (mod 61), but 1155^61 == 2 (mod 34039), therefore this prime is not in the sequence. - Bruno Berselli, Sep 20 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

ok[p_]:= Reduce[Mod[x^61 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[5000]], ok] (* Vincenzo Librandi, Sep 20 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(19000) | forall{x: x in ResidueClassRing(p) | x^61 ne 2} ]; // Vincenzo Librandi, Sep 20 2012

Crossrefs

Cf. A000040, A058853, A212378.

Sequence in context: A307009 A186467 A054827 * A212378 A060518 A065556

Adjacent sequences: A059227 A059228 A059229 * A059231 A059232 A059233

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 20 2001

Status

approved