Open. The site labels the problem OPEN (page last edited 20 January 2026). Its two questions are the problem's two parts. The powers-of-two part is answered no by Kovač and Tao's accepted partial claim. Their Corollary 2.6 (Acta Math. Hungar. 175 (2025)) shows that no strictly increasing sequence with bounded successive ratios is an irrationality sequence of this type. An independent Lean proof by Aristotle is a pending partial claim of the same answer. The factorial part has no claim, and those results do not apply to factorials.