Erdős Problem 346
Is it true that for every lacunary, strongly complete sequence A that is not complete whenever infinitely many terms are removed from it, lim A (n + 1) / A n = (1 + √5) / 2?
Mathematical statement
Is it true that for every lacunary, strongly complete sequence A that is not complete whenever
infinitely many terms are removed from it, lim A (n + 1) / A n = (1 + √5) / 2?
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_346
theorem erdos_346 : answer(sorry) ↔ ∀ {A : ℕ → ℕ}, IsLacunary A → IsAddStronglyCompleteNatSeq A → (∀ B : Set ℕ, B ⊆ range A → B.Infinite → ¬ IsAddComplete (range A \ B)) → Tendsto (fun n => A (n + 1) / (A n : ℝ)) atTop (𝓝 ((1 + √5) / 2)) := 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