A059362 Primes p such that x^24 = 2 has no solution mod p.

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

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: A001097 A117243 A179679 * A212376 A059264 A216484

Adjacent sequences: A059359 A059360 A059361 * A059363 A059364 A059365

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 27 2001

Status

approved