The board / number theory / #243
Erdős Problem #243
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(a_1 < a_2 < \dots\) 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 \(n \ge 1\), \(a_n = a_{n-1}^2 - a_{n-1} + 1\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/243.Prizenone
Topicsnumber theory, irrationality
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA000058
Original pageerdosproblems.com/243
Attempts
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