Question 4
Let $f(n)$ count the ordered expressions of $n$ as a sum of powers of $2$. For example $f(4)=6$, corresponding to $4$, $2+2$, $2+1+1$, $1+2+1$, $1+1+2$, $1+1+1+1$. Find the smallest $n>2013$ for which $f(n)$ is odd.
Proposed by Kiran Kedlaya (credited in the supplied notes).
Proposed by Kiran Kedlaya (credited in the supplied notes).