A049595 Primes p such that x^63 = 2 has a solution mod p.

2, 3, 5, 11, 17, 23, 31, 41, 47, 53, 59, 83, 89, 101, 107, 131, 137, 149, 157, 167, 173, 179, 191, 223, 227, 229, 233, 251, 257, 263, 269, 277, 283, 293, 311, 317, 347, 353, 359, 383, 389, 397, 401, 419, 431, 439, 443, 457, 461, 467, 479, 499, 503, 509, 521

Offset

1,1

Comments

Complement of A059647 relative to A000040. - Vincenzo Librandi, Sep 15 2012

Links

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

Index entries for related sequences

Maple

select(p -> isprime(p) and nops([msolve(x^63-2, p)])>0, [2, seq(2*i+1, i=1..1000)]); # Robert Israel, Nov 03 2014

Mathematica

ok[p_]:= Reduce[Mod[x^63 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[150]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(600) | exists(t){x : x in ResidueClassRing(p) | x^63 eq 2}]; // Vincenzo Librandi, Sep 15 2012
(PARI) N=10^4;
ok(p, r, k)={ return ( (p==r) || (Mod(r, p)^((p-1)/gcd(k, p-1))==1) ); }
forprime(p=2, N, if (ok(p, 2, 63), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A059647.

Sequence in context: A129942 A113239 A049553 * A258039 A107438 A211204

Adjacent sequences: A049592 A049593 A049594 * A049596 A049597 A049598

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved