A049553 Primes p such that x^21 = 2 has a solution mod p.

2, 3, 5, 11, 17, 23, 31, 41, 47, 53, 59, 83, 89, 101, 107, 109, 131, 137, 149, 157, 167, 173, 179, 191, 223, 227, 229, 233, 251, 257, 263, 269, 277, 283, 293, 307, 311, 317, 347, 353, 359, 383, 389, 397, 401, 419, 431, 433, 439, 443, 457, 461, 467, 479, 499

Offset

1,1

Comments

Complement of A059310 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

0^21 == 2 (mod 2). 2^21 == 2 (mod 3). 2^21 == 2 (mod 5). 2^21 == 2 (mod 11). 15^21 == 2 (mod 17). 12^21 == 2 (mod 23). 2^21 == 2 (mod 31). 2^21 == 2 (mod 41). 27^21 == 2 (mod 47). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^21 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[150]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(500) | exists(t){x : x in ResidueClassRing(p) | x^21 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059310.

Sequence in context: A360053 A129942 A113239 * A049595 A258039 A394594

Adjacent sequences: A049550 A049551 A049552 * A049554 A049555 A049556

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved