erdos_263.variants.doubly_exponential_all_but_countable

Koizumi [Ko25] showed that $a_n = \lfloor \alpha^{2^n} \rfloor$ is an irrationality sequence for all but countably many $\alpha > 1$. [Ko25] Koizumi, J., Irrationality of the reciprocal sum of doubly exponential sequences, arXiv:2504.05933 (2025).

theorem erdos_263.variants.doubly_exponential_all_but_countable :
    ∀ᶠ (α : ℝ) in .cocountable, α > 1 → IsIrrationalitySequence (fun n : ℕ => ⌊α ^ 2 ^ n⌋₊)

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