Define $f(0)=1$ and $f(n)$ to be the number of different ways $n$ can be expressed as a sum of integer powers of $2$ using each power no more than twice.
For example, $f(10)=5$ since there are five different ways to express $10$:
$$\begin{align} & 1 + 1 + 8\\ & 1 + 1 + 4 + 4\\ & 1 + 1 + 2 + 2 + 4\\ & 2 + 4 + 4\\ & 2 + 8 \end{align}$$What is $f(10^{25})$?
Solution
No solution yet. Write yours at
solutions/s169.md.