Open. The site labels the problem OPEN (page last edited 2026-04-02). Its two questions are the problem's two parts. The second, whether an irrationality sequence of this kind must satisfy $a_n^{1/n}\to\infty$, has one pending partial claim, a disproof of the growth question posted in 2026, which asserts a counterexample. The first, whether $a_n=2^{2^n}$ is such a sequence, has no claim.