A Threshold for the Best Two-term Underapproximation by Egyptian Fractions

Hung Viet Chu

Let $\mathcal{G}$ be the greedy algorithm that, for each $\theta \in (0,1]$, produces an infinite sequence of positive integers $(a_n{)}_{n=1}^{\infty }$ satisfying $\sum_{n=1}^\infty 1/a_n =…