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Erdős problem 260

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Let a1<a2<⋯a_1 < a_2 < \cdots be an increasing sequence such that ann→∞\frac{a_n}{n} \to \infty. Is the sum ∑n∞an2an\sum_{n}^{\infty} \frac{a_n}{2^{a_n}} irrational?

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