erdos_348

Specification

For what values of $0 \leq m < n$ is there a complete sequence $A = \{a_1 \leq a_2 \leq \cdots\}$ of integers such that 1. $A$ remains complete after removing any $m$ elements, but 2. $A$ is not complete after removing any $n$ elements.

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Lean 4 Statement

theorem erdos_348 :
    { (m, n) | (m) (n) (_ : m < n) (a : ℕ → ℕ) (_ : Monotone a)
      (_ : ∀ s, s.card = m → IsAddComplete (Set.range (Function.updateFinset a s 0)))
        (_ : ∀ t, t.card = n → ¬IsAddComplete (Set.range (Function.updateFinset a t 0))) } =
    answer(sorry)

ID: ErdosProblems__348__erdos_348

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