A049584 Primes p such that x^52 = 2 has a solution mod p.

2, 7, 23, 31, 47, 71, 73, 89, 103, 113, 127, 151, 167, 191, 199, 223, 233, 239, 257, 263, 271, 281, 311, 337, 353, 359, 367, 383, 431, 439, 463, 479, 487, 503, 577, 593, 601, 607, 617, 631, 647, 719, 727, 743, 751, 823, 839, 863, 881, 887, 919, 967, 983, 991

Offset

1,1

Comments

Complement of A059641 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

Mathematica

ok[p_]:= Reduce[Mod[x^52 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1000) | exists(t){x : x in ResidueClassRing(p) | x^52 eq 2}]; // Vincenzo Librandi, Sep 14 2012
(PARI)
N=10^4;  default(primelimit, N);
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, 52), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A059641.

Sequence in context: A072935 A049564 A072936 * A045382 A049560 A049588

Adjacent sequences: A049581 A049582 A049583 * A049585 A049586 A049587

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved