Question 148
Given integer $a_1 \ge 2$, for $n \ge 2$, define $a_n$ to be the least positive integer not coprime to $a_{n-1}$ and not equal to $a_1$, $a_2, \dots, a_{n-1}$. Prove that every integer except $1$ appears in the sequence $\{a_n\}$. (Posed by Yu Hongbing)