A059669 -id:A059669 - cp's OEIS frontend

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

Klaus Brockhaus, Jan 27 2001

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).

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

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

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

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 *)

cp's OEIS Frontend

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

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