erdos_299

Is there an infinite sequence $a_1 < a_2 < \dots$ such that $a_{i+1} - a_i = O(1)$ and no finite sum of $\frac{1}{a_i}$ is equal to 1?

theorem erdos_299 : answer(False) ↔ (∃ (a : ℕ → ℕ),
    StrictMono a ∧ (∀ n, 0 < a n) ∧
    (fun n ↦ (a (n + 1) : ℝ) - a n) =O[atTop] (1 : ℕ → ℝ) ∧
    ∀ S : Finset ℕ, ∑ i ∈ S, (1 : ℝ) / a i ≠ 1)

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