A059666 Primes p such that x^54 = 2 has no solution mod p, but x^18 = 2 has a solution mod p.

3943, 11287, 20143, 23599, 25759, 26407, 29863, 32833, 33751, 38287, 39367, 39799, 46441, 47737, 47791, 59887, 62047, 63127, 68311, 73063, 79273, 82351, 84457, 84673, 88129, 90289, 91639, 93529, 94447, 101089, 104761, 107839, 140617, 144073, 146449, 150607

Offset: 1

Author

Klaus Brockhaus, Feb 05 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..49

Crossrefs

A000040, A049550, A040993.

Programs

Magma

[p: p in PrimesUpTo(40000) | not exists{x: x in ResidueClassRing(p) | x^54 eq 2} and exists{x: x in ResidueClassRing(p) | x^18 eq 2}]; // Vincenzo Librandi, Sep 21 2012

Mathematica

Select[Prime[Range[PrimePi[200000]]],!MemberQ[PowerMod[Range[#],54,#],Mod[2,#]] && MemberQ[PowerMod[Range[#],18,#],Mod[2,#]]&] (* Vincenzo Librandi, Sep 21 2013 *)

Extensions

More terms from Vincenzo Librandi, Sep 21 2013