# Recursive Function

Let $f : \mathbb{N} \rightarrow \mathbb{N}$ be a function defined as follows:

$f(n) = \begin{cases} 1 & n=1 ,\\ f(k) & n = 2k, \\ f(k) + 1 & n = 2k+ 1. \\ \end{cases}$ Let $A$ be the maximum value of $f(n)$ on $1 \leq n \leq 2013$. Calculate the number of values of $n$ with $1 \leq n \leq 2013$ such that $f(n) = A$.

×