Erdős [Er88c] notes that if the sequence grows rapidly to infinity (specifically, if
$a_{n+1} \geq C \cdot a_n^2$ for some constant $C > 0$), then the series is irrational.
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theorem erdos_1051.rapid_growth (a : ℕ → ℤ) (h_mono : StrictMono a)
(h_rapid : ∃ C > 0, ∀ n, (a (n + 1) : ℝ) ≥ C * (a n : ℝ) ^ 2) :
Irrational (ErdosSeries a)
