Erdős problem 263 · problems.science

Must every irrationality sequence $a_n$ in the above sense satisfy $a_n^{1/n} \to \infty$ as $n \to \infty$ ?

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6 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

263.lean

Retained formal statement5 of 6

Kovač and Tao [KoTa24] proved that any strictly increasing sequence $a_n$ such that $\sum \frac{1}{a_n}$ converges and $\lim \frac{a_{n+1}}{a_n^2} = 0$ is not an irrationality sequence in the above sense.

[KoTa24] Kovač, V. and Tao T., On several irrationality problems for Ahmes series. arXiv:2406.17593 (2024).

FormalConjectures/ErdosProblems/263.leanErdos263.erdos_263.variants.sub_doubly_exponential4 linesExact file

1∀ (a : ℕ → ℕ),2  StrictMono a →3    (Summable fun n => 1 / ↑(a n)) →4      Filter.Tendsto (fun n => ↑(a (n + 1)) / ↑(a n) ^ 2) Filter.atTop (nhds 0) → ¬Erdos263.IsIrrationalitySequence a

SolvedStatement only, no proof

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