A059647 Primes p such that x^63 = 2 has no solution mod p.

7, 13, 19, 29, 37, 43, 61, 67, 71, 73, 79, 97, 103, 109, 113, 127, 139, 151, 163, 181, 193, 197, 199, 211, 239, 241, 271, 281, 307, 313, 331, 337, 349, 367, 373, 379, 409, 421, 433, 449, 463, 487, 491, 523, 541, 547, 571, 577, 607, 613, 617, 619, 631, 659

Offset

1,1

Comments

Complement of A049595 relative to A000040.

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^63 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2150]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(700) | not exists{ x : x in ResidueClassRing(p) | x^63 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, 63), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049595.

Sequence in context: A299928 A096452 A258038 * A059310 A299929 A287217

Adjacent sequences: A059644 A059645 A059646 * A059648 A059649 A059650

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved