A059354 Primes p such that x^27 = 2 has no solution mod p, but x^9 = 2 has a solution mod p.

3943, 11287, 12853, 14149, 17659, 20143, 21061, 21277, 23059, 23599, 25759, 26407, 26731, 29863, 32833, 33751, 35803, 37747, 38287, 39367, 39799, 46441, 47737, 47791, 57781, 59887, 61291, 62047, 63127, 65557, 68311, 71443, 73063, 78301

Offset: 1

Author

Klaus Brockhaus, Jan 27 2001

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..107

Crossrefs

Cf. A000040, A049596, A059262, A070185.

Programs

Magma

[ p: p in PrimesUpTo(80000) | exists(t){x: x in ResidueClassRing(p) | x^9 eq 2} and forall(t){x : x in ResidueClassRing(p) | x^27 ne 2} ]; // Klaus Brockhaus, Dec 05 2008

Mathematica

Select[Prime[Range[PrimePi[80000]]], !MemberQ[PowerMod[Range[#], 27, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 9, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 21 2013 *)

Extensions

a(25)-a(34) from Klaus Brockhaus, Dec 05 2008