2017 AMC 12A 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 \qquad\textbf{(B)}\ 2018 \qquad\textbf{(C)}\ 4034 \qquad\textbf{(D)}\ 4035 \qquad\textbf{(E)}\ 4036

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.