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 A163213 Swinging Wilson remainders ((p-1)\$ + (-1)^floor((p+2)/2))/p mod p, p prime. Here '\$' denotes the swinging factorial function (A056040). 4
 1, 1, 1, 3, 1, 6, 9, 13, 12, 2, 19, 2, 5, 36, 6, 19, 43, 11, 47, 67, 39, 41, 70, 12, 17, 83, 88, 81, 25, 53, 91, 97, 106, 79, 43, 39, 7, 29, 73, 6, 79, 115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS If this is zero, p is a swinging Wilson prime. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011. Peter Luschny, Swinging Primes. EXAMPLE The swinging Wilson quotient related to the 5th prime is (252+1)/11=23, so the 5th term is 23 mod 11 = 1. MAPLE WR := proc(f, r, n) map(p->(f(p-1)+r(p))/p mod p, select(isprime, [\$1..n])) end: A002068 := n -> WR(factorial, p->1, n); A163213 := n -> WR(swing, p->(-1)^iquo(p+2, 2), n); MATHEMATICA sf[n_] := n!/Quotient[n, 2]!^2; a[n_] := (p = Prime[n]; Mod[(sf[p - 1] + (-1)^Floor[(p + 2)/2])/p, p]); Table[a[n], {n, 1, 42}] (* Jean-François Alcover, Jun 28 2013 *) PROG (PARI) sf(n)=n!/(n\2)!^2 apply(p->sf(p-1)\/p%p, primes(100)) \\ Charles R Greathouse IV, Dec 11 2016 CROSSREFS Cf. A163211, A002068, A163210. Sequence in context: A089710 A065918 A020861 * A095066 A169955 A084536 Adjacent sequences:  A163210 A163211 A163212 * A163214 A163215 A163216 KEYWORD nonn AUTHOR Peter Luschny, Jul 24 2009 STATUS approved

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Last modified December 2 01:23 EST 2020. Contains 338864 sequences. (Running on oeis4.)