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A059230 Primes p such that x^61 = 2 has no solution mod p. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A142236 A186467 A054827 * A212378 A060518 A065556

Adjacent sequences:  A059227 A059228 A059229 * A059231 A059232 A059233

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 20 2001

STATUS

approved

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Last modified March 19 13:29 EDT 2019. Contains 321330 sequences. (Running on oeis4.)