|
| |
|
|
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.
|
|
|
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
|
|
|
CROSSREFS
|
Cf. A105291.
Sequence in context: A114552 A055706 A118537 * A055702 A179214 A128265
Adjacent sequences: A109889 A109890 A109891 * A109893 A109894 A109895
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 13 2005
|
|
|
EXTENSIONS
|
Corrected and extended by R. J. Mathar, Aug 15 2007
|
|
|
STATUS
|
approved
|
| |
|
|
