MathDB

Let

d(n)

denote the largest odd divisor of a positive integer

n

. The function

f: \mathbb{N} \rightarrow \mathbb{N}

is defined by f(2n\minus{}1)\equal{}2^n and f(2n)\equal{}n\plus{}\frac{2n}{d(n)} for all

n \in \mathbb{N}

. Find all natural numbers

k

such that: f(f(...f(1)...))\equal{}1997. (where the paranthesis appear

k

times)

Problem Statement