Problem 311

Erdős Problem #311: declared status 'open'. Formalized: no. What is the minimal value of $\lvert 1-\sum_{n\in A}\frac{1}{n}\rvert$ as $A$ ranges over all subsets of $\{1,\ldots,N\}$ which contain no $S$ such that $\sum_{n\in S}\frac{1}{n}=1$? Is it$$e^{-(c+o(1))N}$$for some constant $c\in (0,1)$? Prize: no. Tags: number theory, unit fractions.