-RM-

Let f(n) be a function, defined for any integer n <= 0 as follows:

1 if n = 0
f(n) = (f(n/2))^2 if n > 0 and and n is even
2f(n-1) if n > 0 and n is odd

What is the value of f(5)

My working:

2f(4) = 2(f(2))^2 = 2((f(1)^2))^2

I can't figure out what to do next.

The next logical step I can think of for this question is 2((f(1)^2))^2 = 2(((f(0.5)^2)^2)^2)

Sorry for taking a while to get back to you, I was working on other problems and only looked at my computer now :P

The next logical step I can think of for this question is 2((f(1)^2))^2 = 2(((f(0.5)^2)^2)^2)

The issue is that I can just keep going like this, with that number approaching infinity, but never reaching it so I would never actually get to a situation where n = 0. Of course, it does say "for any integer" in the question, but it doesn't specify what to do with non-integers.

... Wow.



Thanks for you help :P