OFFSET
0,3
COMMENTS
1
-------
2*3
..-----
..4*5
....---
....6*.....
In other words, the successive fractions are
1,
1
-,
2
1..4
----,
.23.
1..45.
------,
.23..6
1..45..8
--------,
.23..67.
and so on
Suggested by a question from Ciprian Bonciocat (6 years old).
FORMULA
a(n) = numerator of x(n) where x(0)=1, x(2n+1) = x(2n) (4n+1)/(4n+2), x(2n+2) = x(2n+1)(4n+4)/(4n+3). - Matthew Conroy Jun 26 2006
EXAMPLE
1, 1/2, 2/3, 5/9, 40/63, 4/7, ...
MATHEMATICA
a[0] = 1; a[n_] := a[n] = a[n - 1] If[OddQ[n], (2 n - 1)/(2 n), (2 n)/(2 n - 1)]; A120031[n_] := Numerator[a[n]]; Array[A120031, 26] (* JungHwan Min, Nov 08 2016 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Mihai Cipu (mihai.cipu(AT)imar.ro), Jun 05 2006
EXTENSIONS
More terms from Matthew Conroy, Jun 26 2006
STATUS
approved