A059264 Primes p such that x^12 = 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, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 349, 367, 373, 379, 389

Offset: 1

Author

Klaus Brockhaus, Jan 23 2001

Keywords

• easy
• nonn

Comments

Complement of A049544 relative to A000040.

Coincides for the first 119 terms with sequence of primes p such that x^36 = 2 has no solution mod p (first divergence is at 919, cf. A059668).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A049544, A049568, A059668.

Programs

Mathematica

ok[p_] := Reduce[Mod[x^12 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]],ok] (* Vincenzo Librandi, Sep 14 2012 *)
Select[ Prime@ Range@ PrimePi@400, !MemberQ[ PowerMod[ Range@#, 12, #], Mod[2, #]] &] (* Robert G. Wilson v, Nov 05 2016 after Bruno Berselli in A059362 *)