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erdos_346.example

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Erdős and Graham [ErGr80] also say that it is not hard to construct very irregular sequences satisfying the aforementioned properties.

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Lean 4 Statement 
theorem erdos_346.example : ∃ A : ℕ → ℕ, IsAddStronglyCompleteNatSeq A ∧
    (∀ B : Set ℕ, B ⊆ range A → B.Infinite → ¬ IsAddComplete (range A \ B)) ∧
    liminf (fun n => A (n + 1) / (2 : ℝ)) atTop = 1 ∧
    limsup (fun n => A (n + 1) / (A n : ENNReal)) atTop = ⊤
ID: ErdosProblems__346__erdos_346.example
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