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Problem 839 — Erdős Problems

Problem 839

Let $1\leq a_1<a_2<\cdots$ be a sequence of integers such that no $a_i$ is the sum of consecutive $a_j$ for $j<i$ . Is it true that

\limsup \frac{a_n}{n}=\infty?

Or even

\lim \frac{1}{\log x}\sum_{a_n<x}\frac{1}{a_n}=0?

Source: erdosproblems.com/839

Number theory

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No claim settles this problem.

Open; the site labels the problem OPEN.

Fr93: R. Freud, Adding numbers - on a problem of P. Erdős. James Cook Mathematical Notes (1993), 6199-6202 (the site's key; the issue prints the title "Adding numbers").

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Status: Open
Topics: Number theory
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