For $n\in\mathbb{N}_0$ let $w(n)$ denote the number of $1$s in the binary representation of $n$. For example, $w(9) = 2$, since $9$ is $1001$ in binary. Try to find a closed formula for $g(n)$ in terms of $n$ and $w(n)$. If you succeed, the following question will be very easy. Let $n = 10000000000000011$ in binary notation. What is $g(n)$? Write your answer in binary!
Here $g(n):=f(n!)$ Please Help