A059258 Primes p such that x^53 = 2 has no solution mod p.

107, 743, 1061, 1697, 2333, 2969, 3181, 3499, 3923, 4241, 4877, 5407, 6043, 6361, 6679, 6997, 7103, 7951, 8269, 8693, 9011, 9859, 10177, 10601, 11131, 12721, 13463, 13781, 14629, 14947, 15053, 15583, 15901, 16007, 17491, 17597, 18127, 18233

Offset

1,1

Comments

Complement of A049585 relative to A000040.

Presumably this is also Primes congruent to 1 mod 53 (A212377). - N. J. A. Sloane, Jul 11 2008

Not so. The smallest counterexample is the prime 91373: 91373 == 1 (mod 53), but 2246^53 == 2 (mod 91373), therefore this prime is not in the sequence. - Bruno Berselli, Sep 20 2012

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^53 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok] (* Vincenzo Librandi, Sep 20 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^53 eq 2}]; // Vincenzo Librandi, Sep 20 2012

Crossrefs

Cf. A000040, A049585, A212377.

Sequence in context: A142638 A069759 A183057 * A212377 A113932 A357551

Adjacent sequences: A059255 A059256 A059257 * A059259 A059260 A059261

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 23 2001

Status

approved