The sequence of numbers {Q(m)} is defined recursively by the following relationships:

Q(1) = 1, and:
Q(m) = 1 + Q(m/2), whenever m is ≥ 2 and even, and:
Q(m) = 1/Q(m-1), whenever m is ≥ 3 and odd.

Determine the value of d, given that Q(d) = 19/87

What an interesting function!  Upon quick inspection, it looks to me like this function is a one-to-one mapping between all positive integers and all positive rational numbers.    

Posted by Steve Herman on 2008-02-18 10:50:17