erdos_326

Let $A \subset \mathbb{N}$ be an additive basis of order 2. Must there exist $B = \{b_1 < b_2 < \dots\} \subseteq A$ which is also a basis such that $\lim_{k\to\infty} \frac{b_k}{k^2}$ does not exist?

theorem erdos_326 : answer(sorry) ↔ ∀ (A : Set ℕ), A.IsAddBasisOfOrder 2 →
    ∃ (b : ℕ → ℕ), StrictMono b ∧ ∀ n, b n ∈ A ∧ (Set.range b).IsAddBasis ∧
      ∀ (x : ℝ), ¬ Tendsto (fun n ↦ (b n : ℝ) / n ^ 2) atTop (𝓝 x)

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