A216484 Primes p such that x^36 = 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

Vincenzo Librandi, Sep 14 2012

Keywords

• nonn
• easy

Comments

Complement of A049568 relative to A000040.

Different from A059264: 919, 1423, 1999, ... (see A059668) are terms of this sequence, but not of A059264. [Joerg Arndt, Sep 14 2012]

Coincides for the first 416 terms with the sequence of primes p such that x^108 = 2 has no solution mod p (first divergence is at 3947). [Bruno Berselli, Sep 14 2012]

Links

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

Crossrefs

Cf. A000040, A049568.

Cf. A059668 (primes p such that x^36 = 2 has no solution mod p, but x^12 = 2 has a solution mod p).

Programs

Magma

[p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^36 ne 2}];

Mathematica

ok[p_] := Reduce[Mod[x^36 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[500]], ok]
Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 36, #], Mod[2, #]] &] (* Bruno Berselli, Sep 14 2012 *)