Search: id:A007619
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%I A007619 M4023
%S A007619 1,1,5,103,329891,36846277,1230752346353,336967037143579,48869596859895986087,
%T A007619 10513391193507374500051862069,8556543864909388988268015483871,10053873697024357228864849950022572972973,
%U A007619 19900372762143847179161250477954046201756097561,32674560877973951128910293168477013254334511627907
%N A007619 Wilson quotients: ((p-1)!+1)/p.
%C A007619 Suggested by the Wilson-Lagrange Theorem: An integer p > 1 is a prime 
               if and only if (p-1)! == -1 (mod p).
%C A007619 Define b(n) = ( (n-1)*(n^2-3*n+1)*b(n-1) - (n-2)^3*b(n-2) )/(n*(n-3)); 
               b(2) = b(3) = 1; sequence gives b(primes).
%D A007619 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007619 R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, 
               Springer, NY, 2001; see p. 29.
%D A007619 P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 
               2nd ed., 1989, p. 277.
%D A007619 H. S. Wilf, Problem 10578, Amer. Math. Monthly, 104 (1997), 270.
%H A007619 Achilleas Sinefakopoulos, <a href="http://users.forthnet.gr/ath/asin/
               proandsol.htm">Problem 10578</a>, Submitted solution.
%Y A007619 Cf. A005450, A005451, A007540 (Wilson primes).
%Y A007619 Sequence in context: A052138 A142418 A159523 this_sequence A163212 A163154 
               A165387
%Y A007619 Adjacent sequences: A007616 A007617 A007618 this_sequence A007620 A007621 
               A007622
%K A007619 nonn
%O A007619 1,3
%A A007619 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Mira Bernstein (mira(AT)math.berkeley.edu)

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