Let $1\le a_1<a_2<\cdots$ be a sequence of integers such that$$\mathrm{limsup}\frac{a_n}{n}=\infty .$$Is$$\sum _{n=1}^{\infty }\frac{1}{2^{a_n}}$$transcendental?

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

This is **not known in general**. It is an **open problem of Erdős** (often listed as Erdős Problem #247). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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