OIM 1989 Problem 5

Let the function $f$ be defined on the set $\mathbb{N}$ such that $\text{(i)}\ \ f(1)=1$ $\text{(ii)}\ f(2n+1)=f(2n)+1$ $\text{(iii)} f(2n)=3f(n)$ Determine the set of values taken $f$ .