Question 21
Let $\mathbb{N}$ be the set of positive integers, and let $f: \mathbb{N} \rightarrow \mathbb{N}$ be a function satisfying
- $f(1)=1$;
- for $n \in \mathbb{N}$, $f(2n)=2f(n)$ and $f(2n+1)=2f(n)-1$.
Determine the sum of all positive integer solutions to $f(x)=19$ that do not exceed $2019$.
- $f(1)=1$;
- for $n \in \mathbb{N}$, $f(2n)=2f(n)$ and $f(2n+1)=2f(n)-1$.
Determine the sum of all positive integer solutions to $f(x)=19$ that do not exceed $2019$.