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A130912 Fermat quotients, mod p: ((2^(p-1) - 1)/p) mod p = A007663(n) mod p. 4

%I #22 Feb 21 2022 00:18:22

%S 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,

%T 67,83,18,17,53,30,96,56,82,67,47,3,50,148,50,104,175,135,109,189,201,

%U 68,7,26,142,247,225,128,260,109,70,74,58,78,294,175,120,175,139,153

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

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

%H Amiram Eldar, <a href="/A130912/b130912.txt">Table of n, a(n) for n = 2..10000</a>

%F 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.

%e a(4) = 2 = 9 mod 7 where A007663(4) = 9.

%e The Fermat prime(base 2) for 7 = 9 = (2^6 - 1)/7. Then 9 mod 7 = 2.

%p 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

%t Mod[(2^(#-1)-1)/#,#]&/@Prime[Range[2,70]] (* _Harvey P. Dale_, Mar 31 2013 *)

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

%Y Cf. A007663.

%K nonn

%O 2,2

%A _Gary W. Adamson_, Jun 08 2007

%E More terms from _R. J. Mathar_, Oct 28 2008

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Last modified March 19 09:40 EDT 2024. Contains 370981 sequences. (Running on oeis4.)