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Search: id:A007619
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| A007619 |
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Wilson quotients: ((p-1)!+1)/p.
(Formerly M4023)
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+0
15
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| 1, 1, 5, 103, 329891, 36846277, 1230752346353, 336967037143579, 48869596859895986087, 10513391193507374500051862069, 8556543864909388988268015483871, 10053873697024357228864849950022572972973, 19900372762143847179161250477954046201756097561, 32674560877973951128910293168477013254334511627907
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Suggested by the Wilson-Lagrange Theorem: An integer p > 1 is a prime if and only if (p-1)! == -1 (mod p).
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).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 29.
P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 277.
H. S. Wilf, Problem 10578, Amer. Math. Monthly, 104 (1997), 270.
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LINKS
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Achilleas Sinefakopoulos, Problem 10578, Submitted solution.
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CROSSREFS
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Cf. A005450, A005451, A007540 (Wilson primes).
Adjacent sequences: A007616 A007617 A007618 this_sequence A007620 A007621 A007622
Sequence in context: A123626 A052138 A142418 this_sequence A163212 A163154 A165387
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KEYWORD
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nonn
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AUTHOR
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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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