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

1,1

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

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  *)

Prog

(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

Crossrefs

Cf. A000040, A049550.

Cf. A040993.

Sequence in context: A092729 A290817 A059353 * A040993 A078425 A020587

Adjacent sequences: A212372 A212373 A212374 * A212376 A212377 A212378

Keyword

nonn,easy

Author

Bruno Berselli, Sep 13 2012

Status

approved