A216884 -id:A216884 - cp's OEIS frontend

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

Klaus Brockhaus, Jan 20 2001

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

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

Cf. A000040, A058853, A212378.

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

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

cp's OEIS Frontend

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

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