Claims

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1981_05_11_erdos: Erdős's 1981 note in the Comptes Rendus proves that the sum of a-n over two to the a-n is irrational for every increasing integer sequence whose consecutive gaps tend to infinity, a class of instances of the question.

2026_06_23_wang_grau_ribas: Wang and Grau Ribas's 2026 preprint (later versions by Wang alone) claims that a rational sum of n/2^n over an infinite set has positive density on every large dyadic block, so Problem 260's series is irrational.

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