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A163209
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Wilson spoilers: composite n which divide (n-1)$+(-1)^floor((n+2)/2)). '$' denotes the swinging factorial function (A056040).
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4
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OFFSET
| 1,1
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COMMENTS
| For the factorial function a Wilson spoiler is a composite n that divides (n-1)! + (-1). Lagrange proved that no such n exists. For the swinging factorial the situation is different. 5907 = 3*11*179 was found by S. Skiena. 1194649 = 1093^2 = Sarrus(274) and 12327121 = 3511^2 = Sarrus(824) are pseudoprimes to base 2 (see A001567). 1093 and 3511 are Wieferich primes (A001220). See the Vardi reference for a binomial setup.
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REFERENCES
| Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
I. Vardi, Computational Recreations in Mathematica, 1991, p.66.
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LINKS
| Peter Luschny, Swinging Primes.
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MAPLE
| # swing defined in A163210.
WS := proc(f, r, n) select(p->(f(p-1)+r(p)) mod p = 0, [$2..n]);
select(q -> not isprime(q), %) end:
A163209 := n -> WS(swing, p->(-1)^iquo(p+2, 2), n);
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CROSSREFS
| Cf. A163210, A163213, A007540.
Sequence in context: A061735 A025513 A015295 * A031665 A031575 A031755
Adjacent sequences: A163206 A163207 A163208 * A163210 A163211 A163212
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KEYWORD
| nonn,bref
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Jul 24 2009
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EXTENSIONS
| Typo corrected Peter Luschny (peter(AT)luschny.de), Jul 25 2009
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