A049565 - OEIS

A049565

Primes p such that x^33 = 2 has a solution mod p.

2, 3, 5, 11, 17, 29, 31, 41, 43, 47, 53, 59, 71, 83, 101, 107, 109, 113, 127, 131, 137, 149, 157, 167, 173, 179, 191, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 307, 311, 317, 347, 359, 383, 389, 401, 431, 433, 439, 443, 449, 457

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OFFSET

1,1

COMMENTS

Complement of A059335 relative to A000040. - Vincenzo Librandi, Sep 14 2012

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

EXAMPLE

0^33 == 2 (mod 2). 2^33 == 2 (mod 3). 2^33 == 2 (mod 5). 7^33 == 2 (mod 11). 2^33 == 2 (mod 17). 21^33 == 2 (mod 29). 4^33 == 2 (mod 31). 36^33 == 2 (mod 41). 5^33 == 2 (mod 43). - R. J. Mathar, Jul 20 2025

MATHEMATICA

ok[p_]:= Reduce[Mod[x^33 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

PROG

(Magma) [p: p in PrimesUpTo(500) | exists(t){x : x in ResidueClassRing(p) | x^33 eq 2}]; // Vincenzo Librandi, Sep 14 2012

CROSSREFS

Cf. A000040, A059335.

Sequence in context: A211204 A023206 A359555 * A094480 A215013 A318786

Adjacent sequences: A049562 A049563 A049564 * A049566 A049567 A049568

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved