Question 134
The $f: \mathbb{N} \rightarrow \mathbb{Z}$ function defined as follows is considered: $$
f(n)= \begin{cases}-f\left(\frac{n}{2}\right) & \text{ if } n \text{ It is even } \\ f(n-1)+1 & \text{ if } n \text{ It is odd }\end{cases}
$$ for $n \geq 0$. Prove that $f(n)$ is a multiple of 3 if, and only if, $n$ is a multiple of 3, and find the smallest number $n$ $f(n)=2017$.
f(n)= \begin{cases}-f\left(\frac{n}{2}\right) & \text{ if } n \text{ It is even } \\ f(n-1)+1 & \text{ if } n \text{ It is odd }\end{cases}
$$ for $n \geq 0$. Prove that $f(n)$ is a multiple of 3 if, and only if, $n$ is a multiple of 3, and find the smallest number $n$ $f(n)=2017$.