A sequence of natural numbers is constructed by listing the first $5$, then skipping $2$, listing the next $6$, skipping $3$, and on the $n$th iteration, listing $n+4$ and skipping $n+1$. The sequence begins $1,2,3,4,5,8,9,10,11,12,13,17$. What is the $600,000$th number in the sequence?