A059645 Primes p such that x^60 = 2 has no solution mod p.

3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347

Offset

1,1

Comments

Complement of A049592 relative to A000040.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

ok[p_] := Reduce[Mod[x^60 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(400) | not exists{x: x in ResidueClassRing(p) | x^60 eq 2}]; // Vincenzo Librandi, Sep 21 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, 60), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049592.

Sequence in context: A225669 A065389 A123567 * A090190 A325143 A276357

Adjacent sequences: A059642 A059643 A059644 * A059646 A059647 A059648

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved