2014 AMC 10A 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 nth 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^{\text{th}} number in the sequence?

\textbf{(A)}\ 996,506\qquad\textbf{(B)}\ 996,507\qquad\textbf{(C)}\ 996,508\qquad\textbf{(D)}\ 996,509\qquad\textbf{(E)}\ 996,510

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