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A109892
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a(n) = least integer of the form (n!+1)(n!+2)...(n!+k)/n!.
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3
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OFFSET
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1,1
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COMMENTS
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Equivalently, binomial(n!+n,n). Proof: (n!+1)(n!+2)...(n!+k) == k! mod n! == 0 mod n! if and only if k >= n (for n >= 2). - Paul D Hanna and Robert Israel, Aug 31 2010.
Note that k <= n. Subsidiary sequence to be investigated: n such that k < n.
This is just a coincidence, but k=2,6,84 are also such that floor(exp(1)*10^k) is a prime, cf. A064118. - M. F. Hasler, Aug 31 2013
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LINKS
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Table of n, a(n) for n=1..9.
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EXAMPLE
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a(4)=25*26*27*28/24=20475.
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MAPLE
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A109892 := proc(n) local k, fn; k := 1; fn := n! ; while mul(fn+i, i=1..k) mod fn <> 0 do k := k+1; od ; RETURN(mul(fn+i, i=1..k)/fn) ; end: seq(A109892(n), n=1..10) ; - R. J. Mathar, Aug 15 2007
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MATHEMATICA
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Table[(n+n!)!/(n!*(n!)!), {n, 1, 9}] (* Jean-François Alcover, Mar 04 2014, after first comment *)
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CROSSREFS
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Cf. A105291.
Sequence in context: A114552 A055706 A118537 * A055702 A179214 A128265
Adjacent sequences: A109889 A109890 A109891 * A109893 A109894 A109895
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KEYWORD
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nonn,changed
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AUTHOR
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Amarnath Murthy, Jul 13 2005
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EXTENSIONS
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Corrected and extended by R. J. Mathar, Aug 15 2007
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STATUS
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approved
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