Problem 347

Erdős Problem #347: declared status 'proved'. Formalized: yes. 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 $A$? Prize: no. Tags: complete sequences, number theory.