

A109892


a(n) = least integer of the form (n!+1)(n!+2)...(n!+k)/n!.


3




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}] (* JeanFrançois 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



