Problem 243

Erdős Problem #243: declared status 'open'. Formalized: yes. Let $a_1<a_2<\cdots$ be a sequence of integers such that$$\lim_{n\to \infty}\frac{a_n}{a_{n-1}^2}=1$$and $\sum\frac{1}{a_n}\in \mathbb{Q}$. Then, for all sufficiently large $n\geq 1$,$$a_n = a_{n-1}^2-a_{n-1}+1.$$ Prize: no. OEIS: A000058. Tags: number theory.