I think what you need is something that is at least as large as the largest Fibonaci number you are going to compute. Since the Fibonnaci numbers grow as `phi^n

I think what you need is something that is at least as large as the largest Fibonaci number you are going to compute. Since the Fibonnaci numbers grow as `phi^n` where `phi` is the golden ratio (~= 1.618) if you want to use something of the form `A*b^n` you need `b >= phi` and to pick A to make it work out for small `n`. So, if you want integer `b` then 2 is the smallest you can do. But you could also do `b=1.7` or something like `A*17^n/10^n` if you want to use only integers.