erdos_341

Let $A=\{a_1 < \cdots < a_k\}$ be a finite set of integers and extend it to an infinite sequence $\overline{A}=\{a_1 < a_2 < \cdots \}$ by defining $a_{n+1}$ for $n \geq k$ to be the least integer exceeding $a_n$ which is not of the form $a_i + a_j$ with $i,j \leq n$. Is it true that the sequence of differences $a_{m+1}-a_m$ is eventually periodic? This problem is discussed under Problem 7 on Green's open problems list.

theorem erdos_341 :
    answer(sorry) ↔
      ∀ (a : ℕ → ℤ),
        (∀ᶠ n in atTop,
          IsLeast { x | a n < x ∧ x ∉ { a i + a j | (i ≤ n) (j ≤ n) } } (a (n + 1))) →
        let d

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