AMC 12 2017a Problem 7

Define a function on the positive integers recursively by $f(1) = 2$, $f(n) = f(n-1) + 1$ if $n$ is even, and $f(n) = f(n-2) + 2$ if $n$ is odd and greater than $1$. What is $f(2017)$?

\textbf{(A)}\ 2017 \textbf{(B)}\ 2018 \textbf{(C)}\ 4034 \textbf{(D)}\ 4035 \textbf{(E)}\ 4036