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A059258 Primes p such that x^53 = 2 has no solution mod p. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A250154

Adjacent sequences:  A059255 A059256 A059257 * A059259 A059260 A059261

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 23 2001

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)