Problem Statement
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 $1$?
Categories:
Number Theory Unit Fractions
Progress
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.
Source: erdosproblems.com/299 | Last verified: January 14, 2026