Question 3
Consider an infinite sequence $a_0, a_1, a_2, \dots$ of integers that satisfies
$$
a_0 \ge 1 \quad \text{and} \quad a_{n+1} \in \{2022a_n - 1, 2022a_n + 1\}
$$
for all indices $n \ge 0$. Prove that any such infinite sequence contains infinitely many composite numbers.
(Martin Melicher)
$$
a_0 \ge 1 \quad \text{and} \quad a_{n+1} \in \{2022a_n - 1, 2022a_n + 1\}
$$
for all indices $n \ge 0$. Prove that any such infinite sequence contains infinitely many composite numbers.
(Martin Melicher)