Erdős Problem #1051

declared status 'proved'. Formalized: yes. Is it true that if $a_1<a_2<\cdots$ is a sequence of integers with$$\liminf a_n^{1/2^n}>1$$then$$\sum_{n=1}^\infty \frac{1}{a_na_{n+1}}$$is irrational? Prize: no. Tags: irrationality.

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