MathNet 2020 — Math Olympiad Vault — Part 05 Question 139

Consider a real number $a \ge 1$. The sequence $(x_n)_{n \ge 1}$ is given by $x_1 = a$ and $x_{n+1} = 1 + \log_2 x_n$, for any $n \in \mathbb{N}^*$. Determine values of $a$ such that all terms of the sequence are rational numbers.