|
Search: id:A124781
|
|
|
| A124781 |
|
GCD(d(n), d(n+2)) where d(n) = GCD(n!, A(n)) and A(n) = A000522(n) = Sum_{k=0..n} n!/k!). |
|
+0
4
|
|
| 1, 1, 1, 2, 1, 2, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 2, 1, 2, 5, 26, 1, 2, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 13, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 26, 1, 2, 5, 2, 1, 2, 1, 10, 1, 2, 1, 2, 65, 2, 1, 2, 1, 10, 1, 2, 1, 74, 5, 2, 1, 26, 1, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 13, 2, 1, 2, 5, 2, 1, 2, 1
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
a(n) divides n+3 because A(n+2) = (n+2)(n+1)*A(n) + n+3.
|
|
REFERENCES
|
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
|
|
LINKS
|
Index entries for sequences related to factorial numbers
|
|
FORMULA
|
a(n) = GCD(A093101(n), A093101(n+2)) = (n+3)/A123901(n)
a(n) = GCD(A(n), A(n+2), n!) where A(n)=1+n+n(n-1)+...+n! - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Nov 13 2006
|
|
EXAMPLE
|
a(3) = GCD(d(3),d(5)) = GCD(GCD(3!,16), GCD(5!,326)) = GCD(2,2) =
2
|
|
MATHEMATICA
|
(A[n_] := Sum[n!/k!, {k, 0, n}]; d[n_] := GCD[n!, A[n]]; Table[GCD[d[n], d[n+2]], {n, 0, 100}])
|
|
CROSSREFS
|
Cf. A000522, A093101, A123899, A123900, A123901, A124779, A124780, A124782.
Sequence in context: A066772 A104060 A062347 this_sequence A124151 A110179 A071559
Adjacent sequences: A124778 A124779 A124780 this_sequence A124782 A124783 A124784
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Nov 07 2006
|
|
|
Search completed in 0.002 seconds
|
