Question 13
Let $n$ be a natural number. We define $f(n)$ as the number of ways of writing $n$ as a sum of powers of 2, where the order in which each term appears is taken into account. For example, $f(4) = 6$ because $4$ can be written as $4$; $2+2$; $2+1+1$; $1+2+1$; $1+1+2$; $1+1+1+1$.
Find the smallest $n$ greater than $2019$ for which $f(n)$ is odd.
Find the smallest $n$ greater than $2019$ for which $f(n)$ is odd.