A130912 Fermat quotients, mod p: ((2^(p-1) - 1)/p) mod p = A007663(n) mod p.

1, 3, 2, 5, 3, 13, 3, 17, 1, 6, 1, 23, 25, 44, 36, 8, 36, 10, 2, 56, 19, 48, 6, 57, 92, 59, 13, 67, 83, 18, 17, 53, 30, 96, 56, 82, 67, 47, 3, 50, 148, 50, 104, 175, 135, 109, 189, 201, 68, 7, 26, 142, 247, 225, 128, 260, 109, 70, 74, 58, 78, 294, 175, 120, 175, 139, 153

Offset: 2

Author

Gary W. Adamson, Jun 08 2007

Keywords

• nonn

Examples

			a(4) = 2 = 9 mod 7 where A007663(4) = 9.
The Fermat prime(base 2) for 7 = 9 = (2^6 - 1)/7. Then 9 mod 7 = 2.
		

References

• Paulo Ribenboim, "The Little Book of Bigger Primes", Springer-Verlag, 2004, p. 232.

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A007663.

Programs

Maple

a := 2 : for n from 2 to 120 do p := ithprime(n) ; fq := (a^(p-1)-1)/p ; printf("%d,",fq mod p) ; od: # R. J. Mathar, Oct 28 2008

Mathematica

Mod[(2^(#-1)-1)/#,#]&/@Prime[Range[2,70]] (* Harvey P. Dale, Mar 31 2013 *)

PARI

forprime(p=3, 1e3, my(t=(2^(p-1)-1)/p); print1(t%p, ", ")); \\ Felix Fröhlich, Jul 26 2014

Formula

Fermat quotients mod p = A007663: (1, 3, 9, 93, 315, ...) mod p; where the Fermat quotients for base 2 = (2^(p-1) - 1). Applies to the odd primes.

Extensions

More terms from R. J. Mathar, Oct 28 2008