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A059362 Primes p such that x^24 = 2 has no solution mod p. 5
3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A049556 relative to A000040.

Coincides for the first 23 terms with sequence A059264 of primes p such that x^12 = 2 has no solution mod p (first divergence is at 113, cf. A059331).

Coincides for the first 161 terms with sequence A212376 of primes p such that x^48 = 2 has no solution mod p (first divergence is at 1217, cf. A059669).

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

MATHEMATICA

Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 24, #], Mod[2, #]] &] (* Bruno Berselli, Sep 14 2012 *)

ok[p_] := Reduce[Mod[x^24 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 20 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^24 ne 2}]; // Bruno Berselli, Sep 14 2012

CROSSREFS

Cf. A000040, A049556, A059264, A059331, A059669, A212376.

Sequence in context: A117243 A179679 * A212376 A059264 A216484 A179479

Adjacent sequences:  A059359 A059360 A059361 * A059363 A059364 A059365

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 27 2001

STATUS

approved

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Last modified February 22 21:02 EST 2018. Contains 299469 sequences. (Running on oeis4.)