A049556 Primes p such that x^24 = 2 has a solution mod p.

2, 23, 31, 47, 71, 89, 127, 167, 191, 223, 233, 239, 257, 263, 311, 359, 383, 431, 439, 479, 503, 599, 601, 647, 719, 727, 743, 839, 863, 881, 887, 911, 919, 983, 1031, 1103, 1151, 1217, 1223, 1289, 1319, 1327, 1367, 1399, 1423, 1433, 1439, 1471, 1487, 1511

Offset

1,1

Comments

Complement of A059362 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

0^24 == 2 (mod 2). 5^24 == 2 (mod 23). 3^24 == 2 (mod 31). 2^24 == 2 (mod 47). 24^24 == 2 (mod 71). 25^24 == 2 (mod 89). 5^24 == 2 (mod 127). 63^24 == 2 (mod 167). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^24 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1600) | exists(t){x : x in ResidueClassRing(p) | x^24 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059362.

Sequence in context: A107153 A049544 A049568 * A049580 A373780 A061448

Adjacent sequences: A049553 A049554 A049555 * A049557 A049558 A049559

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved