Claims

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2024_11_05_van_doorn: Van Doorn's 2024 arXiv paper proves that the denominator of a block of consecutive reciprocals starting at a first drops at an index at most linear in a, and that the drop comes after at least order log a terms.

2026_08_31_van_doorn: A 2026 preprint claims that the limit inferior of (b(a) - a)/log a equals 1/(1+c), about 0.546, the lower value of the author's 2024 bounds, with a language model credited for one step.

2026_09_24_van_doorn: A 2026 note claims that for almost all a the first denominator drop comes after more than exp((1/2) sqrt(log a log log a)) terms, so no power of log a bounds b(a) - a on a set of positive density.

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