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A059645
Primes p such that x^60 = 2 has no solution mod p.
2
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
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
Sequence in context: A225669 A065389 A123567 * A090190 A325143 A276357
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Feb 02 2001
STATUS
approved