Claims

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2024_11_27_kovac_tao: Kovač and Tao construct a strictly increasing integer sequence with both reciprocal sums rational and a_n^(1/beta^n) tending to infinity for any base beta below the square root of 6/5; the exact exponent is not determined.

2026_08_28_cam: A 2026 write-up posted to the problem's proof-claims thread asserts a construction, for every beta below (sqrt(13)-1)/2, of an increasing integer sequence with both reciprocal sums rational and a_n^(1/beta^n) unbounded.

2026_09_07_kitamura: Kenta Kitamura's Lean 4 development, developed with ChatGPT and OpenAI Codex using GPT-6 (Astra), claims that no increasing sequence with both reciprocal sums rational has limsup of a_n^(1/2^n) above 1; the exact exponent is open.

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