Source labels openChecked July 26, 2026

Erdős Problem 359: Ii

Let $a_1< a_2 < ⋯$ be an infinite sequence of integers such that $a_1=1$ and $a_{i+1}$ is the least integer which is not a sum of consecutive earlier $a_j$ s. Show that $a_k / k ^ {1 + c} \to 0$ for any $c > 0$ .

Number theory AMS 11

Mathematical statement

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_359.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_359.parts.ii (A : ℕ → ℕ) (hA : IsGoodFor A 1) (c : ℝ) (hc : 0 < c):    atTop.Tendsto (fun k ↦ A k / (k : ℝ) ^ (1 + c)) (nhds 0) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/359background