Problem #10: Compose until

For an integer \(n \in \mathbb N^*\), let \(d(n)\) be the greatest odd divisor of \(n\).

And let \(f : \mathbb N^* \to \mathbb N\) such that

$$f(2n-1) = 2^n \quad \text{and} \quad f(2n) = n + \dfrac{2n}{d(n)}$$

Find the sum of all integers \(k\) such that \(\underbrace{f(f(...f(1)...))}_{k \; \text{times}} = 2015\)