On a conjecture of Erdős and Graham about the Sylvester's sequence

Zheng Li, Quanyu Tang

Let $\{u_n{\}}_{n=1}^{\infty }$ be the Sylvester's sequence (sequence A000058 in the OEIS), and let $a_1<a_2<\cdots$ be any other positive integer sequence satisfying $ \sum_{i=…