Counting

Consider the sequence $a_1,a_2,a_3,a_4...$ such that $a_1=2$ and for every positive integer $n$, $a_{n+1}=a_n+p_n$, where $p_n$ is the largest prime factor of $a_n$. The first few terms of the sequence are $2,4,6,9,12,15,20$. What is the largest value of $n$ such that $a_n$ is a four-digit number?