A212375 Primes p such that x^18 = 2 has no solution mod p.

3, 5, 7, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 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, 397

Offset: 1

Author

Bruno Berselli, Sep 13 2012

Keywords

• nonn
• easy

Comments

Complement of A049550 relative to A000040.

This sequence is not the same as A040993. First disagreement at index 59: a(59)=433, A040993(59)=443.

Links

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

Crossrefs

Cf. A000040, A049550.

Cf. A040993.

Programs

Magma

[p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^18 ne 2}];

Magma

[p: p in PrimesUpTo(400) | not exists{x : x in ResidueClassRing(p) | x^18 eq 2} ]; // Vincenzo Librandi, Sep 20 2012

Mathematica

Select[Prime[Range[PrimePi[500]]], ! MemberQ[PowerMod[Range[#], 18, #], Mod[2, #]] &]
ok[p_]:= Reduce[Mod[x^18 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 20 2012  *)