OPEN
This is open, and cannot be resolved with a finite computation.
Is there a sequence $A=\{a_1\leq a_2\leq \cdots\}$ of integers with\[\lim \frac{a_{n+1}}{a_n}=2\]such that\[P(A')= \left\{\sum_{n\in B}n : B\subseteq A'\textrm{ finite }\right\}\]has density $1$ for every cofinite subsequence $A'$ of $A$?
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 #347, https://www.erdosproblems.com/347, accessed 2026-01-16
