A059642 Primes p such that x^55 = 2 has no solution mod p.

11, 23, 31, 41, 61, 67, 71, 89, 101, 131, 181, 191, 199, 211, 271, 281, 311, 331, 353, 397, 401, 419, 421, 461, 463, 491, 521, 541, 601, 617, 631, 661, 683, 691, 701, 727, 751, 761, 811, 821, 859, 881, 941, 947, 991, 1021, 1031, 1051, 1061, 1091, 1123

Offset

1,1

Comments

Complement of A049587 relative to A000040.

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^55 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1150) | not exists{x: x in ResidueClassRing(p) | x^55 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, 55), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049587.

Sequence in context: A337845 A030675 A110786 * A090920 A344175 A126330

Adjacent sequences: A059639 A059640 A059641 * A059643 A059644 A059645

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved