A146211 Fermat quotient of the n-th prime with base 3.

16, 104, 5368, 40880, 2532160, 20390552, 1364393896, 788854912240, 6641649422408, 4056611764783760, 296528425830656800, 2544627654221217656, 188573151481968108424, 121907205457107043376080

Offset: 3

Author

R. J. Mathar, Oct 28 2008

Keywords

• easy
• nonn

Links

• Takashi Agoh and Ladislav Skula, The fourth power of the Fermat quotient, J. Numb. Theory 128 (2008) 2865-2873.

Crossrefs

Subsequence of A046211. Cf. A007663.

Programs

Maple

A146211:= n-> map (p-> (3^(p-1)-1)/p, ithprime(n)):
seq (A146211(n), n=3..16); # Jani Melik, Jan 24 2010

Mathematica

Table[(3^(p - 1) - 1)/p, {p, Prime[Range[3, 16]]}] (* Amiram Eldar, Oct 13 2023 *)

PARI

a(n) = my(p=prime(n)); (3^(p-1)-1)/p; \\ Michel Marcus, Oct 13 2023

Formula

a(n) = (3^(p-1)-1)/p, where p=A000040(n).

a(n) = A046211(A000040(n)), for n >= 3. - Amiram Eldar, Oct 13 2023