Function from integers to integers

Number Theory Level 5

Let \(f:\mathbb{N} \rightarrow \mathbb{N}\) be a function such that \(f(1)= 1\), and for all positive integers \(n,\) \(f(2n)= f(n)\) and \(f(2n+1)= f(n) + f(n+1)\). Find the number of odd integers \(n\) such that \(f(n)= 2015\).

Details and assumptions