Question 121
The numbers $1, 2, \ldots, 2002$ are written in order on a blackboard. Then the 1st, 4th, 7th, $\ldots$, $3k+1$th, $\ldots$ numbers in the list are erased. Then the 1st, 4th, 7th, $\ldots$, $3k+1$th numbers in the remaining list are erased (leaving $3, 5, 8, 9, 12, \ldots$). This process is carried out repeatedly until there are no numbers left. What is the last number to be erased?