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A109892 a(n) = least integer of the form (n!+1)(n!+2)...(n!+k)/n!. 3
2, 6, 84, 20475, 234531275, 199200973555045, 16481425431663122588749, 173392935733620216899469862542865, 300717095810709134168380432250652303057474577 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

a(4)=25*26*27*28/24=20475.

MAPLE

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

MATHEMATICA

Table[(n+n!)!/(n!*(n!)!), {n, 1, 9}] (* Jean-Fran├žois Alcover, Mar 04 2014, after first comment *)

CROSSREFS

Cf. A105291.

Sequence in context: A245463 A055706 A118537 * A055702 A179214 A128265

Adjacent sequences:  A109889 A109890 A109891 * A109893 A109894 A109895

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jul 13 2005

EXTENSIONS

Corrected and extended by R. J. Mathar, Aug 15 2007

STATUS

approved

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Last modified November 24 04:08 EST 2014. Contains 249867 sequences.