erdos_263.variants.sub_doubly_exponential

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).

theorem erdos_263.variants.sub_doubly_exponential (a: ℕ -> ℕ)
    (ha' : StrictMono a)
    (ha'' : Summable (fun n : ℕ => 1 / (a n : ℝ)))
    (ha''' : atTop.Tendsto (fun n : ℕ => (a (n + 1) : ℝ) / a n ^ 2) (𝓝 0)) :
    ¬ IsIrrationalitySequence a

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