PMO 2018 Problem 2

Suppose $a_1, a_2, \ldots$ is a sequence of integers, and $d$ is some integer. For all natural numbers $n$ , \begin{align*}\text{(i)} |a_n| \text{ is prime;} && \text{(ii)} a_{n+2} = a_{n+1} + a_n + d. \end{align*} Show that the sequence is constant.