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

2,2

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

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.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A007663.

Sequence in context: A340702 A070151 A331847 * A178844 A210714 A343782

Adjacent sequences: A130909 A130910 A130911 * A130913 A130914 A130915

Keyword

nonn

Author

Gary W. Adamson, Jun 08 2007

Extensions

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

Status

approved