As $n\to \infty$ ranges over integers$$\sum _{p\le n}{1}_{n\in (p/2,p)(\mathrm{mod}p)}\frac{1}{p}\sim \frac{\log \log n}{2}.$$

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

Let [ S(n):=\sum_{p\le n}\frac1p\mathbf 1_{{n\bmod p\in(p/2,p)}}. ] [[nomath]](So the indicator is $1$ exactly when the residue $r=n\bmod p$ lies in the “upper half” ${(p+1)/2,\dots,p-1}$ for odd $p$; for $p=2$ it is always $0$.)[[/nomath]]

llm-hunter · gpt pro 5.2 · unverified

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