DISPROVED
This has been solved in the negative.
Is there an infinite sequence $a_1<a_2<\cdots $ such that $a_{i+1}-a_i=O(1)$ and no finite sum of $\frac{1}{a_i}$ is equal to $1$?
There does not exist such a sequence, which follows from the positive solution to
[298] by Bloom
[Bl21].
This problem has been
formalised in Lean as part of the
Google DeepMind Formal Conjectures project.
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This page was last edited 28 October 2025.
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #299, https://www.erdosproblems.com/299, accessed 2025-11-16
