Claims

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2025_04_25_crmaric_kovac: Crmarić and Kovač show that for every positive real alpha some f tending to infinity makes the series equal alpha, so the sum need not be irrational.

2026_08_22_lambrinoudis: A manuscript of August 2026 by Costa Lambrinoudis, written with generative AI, proves the sum irrational for f(n) = an + b with a >= 1 and 0 <= b <= a, and claims transcendence, hence irrationality, for every b >= 1 - a.

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