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Search: id:A163213
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| A163213 |
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Swinging Wilson remainders ((p-1)$ + (-1)^floor((p+2)/2))/p mod p, p prime. Here '$' denotes the swinging factorial function (A056040). |
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+0
5
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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If this is zero, p is a swinging Wilson prime.
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REFERENCES
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Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
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Peter Luschny, Swinging Primes.
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EXAMPLE
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The swinging Wilson quotient related to the 5th prime is (252+1)/11=23, so the 5th term is 23 mod 11 = 1.
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MAPLE
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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);
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CROSSREFS
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Cf. A163211, A002068, A163210.
Sequence in context: A089710 A065918 A020861 this_sequence A095066 A084536 A110770
Adjacent sequences: A163210 A163211 A163212 this_sequence A163214 A163215 A163216
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KEYWORD
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nonn
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Jul 24 2009
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