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A163210 Swinging Wilson quotients ((p-1)$ +(-1)^floor((p+2)/2))/p, p prime. Here '$' denotes the swinging factorial function (A056040). 6
1, 1, 1, 3, 23, 71, 757, 2559, 30671, 1383331, 5003791, 245273927, 3362110459, 12517624987, 175179377183, 9356953451851, 509614686432899, 1938763632210843, 107752663194272623 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

M. E. Bassett, S. Majid, Finite noncommutative geometries related to F_p[x], arXiv preprint arXiv:1603.00426, 2016

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..470

Peter Luschny, Swinging Primes.

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.

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);

MATHEMATICA

sf[n_] := n!/Quotient[n, 2]!^2; a[n_] := (p = Prime[n]; (sf[p - 1] + (-1)^Floor[(p + 2)/2])/p); Table[a[n], {n, 1, 19}] (* Jean-Fran├žois Alcover, Jun 28 2013 *)

PROG

(PARI) a(n, p=prime(n))=p!/(p\2)!^2 \\ Charles R Greathouse IV, Dec 10 2016

CROSSREFS

Cf. A163213, A002068, A163212, A163209, A007619, A007540.

Sequence in context: A121984 A107177 A096207 * A163211 A126335 A256329

Adjacent sequences:  A163207 A163208 A163209 * A163211 A163212 A163213

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 24 2009

STATUS

approved

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Last modified April 28 12:38 EDT 2017. Contains 285575 sequences.