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A163210
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Swinging Wilson quotients ((p-1)$ +(-1)^floor((p+2)/2))/p, p prime. Here '$' denotes the swinging factorial function (A056040).
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7
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1, 1, 1, 3, 23, 71, 757, 2559, 30671, 1383331, 5003791, 245273927, 3362110459, 12517624987, 175179377183, 9356953451851, 509614686432899, 1938763632210843, 107752663194272623
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
| Peter Luschny, Swinging Primes.
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EXAMPLE
| The 5th prime is 11, (11-1)$ = 252, the remainder term is (-1)^floor((11+2)/2)=1. So the quotient (252+1)/11 = 23 is the 5th member of the sequence.
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MAPLE
| swing := proc(n) option remember; if n = 0 then 1 elif irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
WQ := proc(f, r, n) map(p->(f(p-1)+r(p))/p, select(isprime, [$1..n])) end:
A163210 := n -> WQ(swing, p->(-1)^iquo(p+2, 2), n);
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CROSSREFS
| Cf. A163213, A002068, A163212, A163209, A007619, A007540.
Sequence in context: A121984 A107177 A096207 * A163211 A126335 A196649
Adjacent sequences: A163207 A163208 A163209 * A163211 A163212 A163213
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Jul 24 2009
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