Problem 243

Let $1\leq a_1<a_2<\cdots$ 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.

Status

Open

No claim settles this problem.

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