Question 33
Let $n \gt 1$ be a positive integer. The first term of the infinite progression $(a_k)$ of positive integers is $a_1 = n$. For all $k \gt 1$ we have either $a_k = 2a_{k-1} + 1$ or $a_k = 2a_{k-1} - 1$. Prove that not all terms of this progression are prime numbers.