

A130912


Fermat quotients, mod p: ((2^(p1)  1)/p) mod p = A007663(n) mod p.


2



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
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OFFSET

2,2


REFERENCES

Paulo Ribenboim, "The Little Book of Bigger Primes", SpringerVerlag, 2004, p. 232.


LINKS

Table of n, a(n) for n=2..68.


FORMULA

Fermat quotients mod p = A007663: (1, 3, 9, 93, 315,...) mod p; where the Fermat quotients for base 2 = (2^(p1)  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^(p1)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^(p1)1)/p); print1(t%p, ", ")); \\ Felix FrÃ¶hlich, Jul 26 2014


CROSSREFS

Cf. A007663.
Sequence in context: A131025 A070151 * A178844 A210714 A143956 A110661
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



