Erdős Problem #347

The problem

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 $A$?

Statement quoted from erdosproblems.com/347, maintained by Thomas Bloom. Original source: [ErGr80]. Current status there: proved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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