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A193447
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a(n) = ((p - 2)! + p - 1)/(p*(p - 1)) where p is the n-th prime.
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2
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3, 3299, 255877, 4807626353, 1040021719579, 100970241446066087, 13409937746820630739862069, 9507270961010432209186683871, 7757618593382991688938927430572972973, 12437732976339904486975781548721278876097561, 18522993694996570934756402022946152638511627907
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OFFSET
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4,1
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COMMENTS
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Conjecture: for k >= 7, ((k - 2)! + k - 1)/(k*(k - 1)) is an integer iff k is prime.
Proof follows from Wilson's theorem. - Alois P. Heinz, Aug 07 2011
Note that a(1) = 1 is also an integer. - Jianing Song, Sep 17 2018
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LINKS
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Table of n, a(n) for n=4..14.
Wikipedia, Wilson's theorem
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EXAMPLE
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a(4) = (5! + 6)/(7*6) = 126/42 = 3.
a(5) = (9! + 10)/(11*10) = 362890/110 = 3299.
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PROG
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(PARI) a(n) = my(p=prime(n)); ((p-2)!+p-1)/(p*(p-1)) \\ Jianing Song, Sep 17 2018
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CROSSREFS
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Cf. A000040, A007619, A066161.
Sequence in context: A281928 A036520 A359130 * A134909 A286215 A259157
Adjacent sequences: A193444 A193445 A193446 * A193448 A193449 A193450
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KEYWORD
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nonn
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AUTHOR
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Alzhekeyev Ascar M, Jul 26 2011
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EXTENSIONS
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Name clarified by Jianing Song, Sep 17 2018
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STATUS
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approved
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