Question 43
Determine the function $f: \mathbb{N} \rightarrow \mathbb{N}$ ($\mathbb{N}=\{1,2,3, \ldots\}$ being the set of natural numbers) that satisfies, for any $s, n \in \mathbb{N}$, the following conditions:
$f(1)=f\left(2^{s}\right)=1$ and if $n\lt 2^{s}$, then $f\left(2^{s}+n\right)=f(n)+1$.
Calculate the maximum value of $f(n)$ when $n \leq 2001$.
Find the smallest natural number $n$ such that $f(n)=2001$.
$f(1)=f\left(2^{s}\right)=1$ and if $n\lt 2^{s}$, then $f\left(2^{s}+n\right)=f(n)+1$.
Calculate the maximum value of $f(n)$ when $n \leq 2001$.
Find the smallest natural number $n$ such that $f(n)=2001$.