AMC 10 2014a Problem 24

A sequence of natural numbers is constructed by listing the first $4$, then skipping one, listing the next $5$, skipping $2$, listing $6$, skipping $3$, and on the $n$th iteration, listing $n+3$ and skipping $n$. The sequence begins $1,2,3,4,6,7,8,9,10,13$. What is the $500, 000$th number in the sequence? $\textbf{(A)}\ 996, 506 \textbf{(B)}\ 996, 507 \textbf{(C)}\ 996, 508 \textbf{(D)}\ 996, 509 \textbf{(E)}\ 996, 510$