Let $\delta (N)$ be the minimal non-zero value of $|1-{\sum }_{n\in A}\frac{1}{n}|$ as $A$ ranges over all subsets of $\{1,\dots ,N\}$. Is it true that$$\delta (N)=e^{-(c+o(1))N}$$for some constant $c\in (0,1)$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

[ \delta(N)\ :=\ \min\\{|1-\sum_{n\in A}\frac1n|\ :\ A\subseteq{1,\dots,N}\\}\cap(0,\infty). ]

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.