OPEN
This is open, and cannot be resolved with a finite computation.
Is it true that if $a_1<a_2<\cdots$ is a sequence of integers with\[\liminf a_n^{1/2^n}>1\]then\[\sum_{n=1}^\infty \frac{1}{a_na_{n+1}}\]is irrational?
In
[Er88c] Erdős notes this is true if $a_n\to \infty$ 'rapidly'.
View the LaTeX source
This page was last edited 29 September 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 #1051, https://www.erdosproblems.com/1051, accessed 2025-11-16
