All open problems
Source labels openChecked July 26, 2026
Erdős Problem 342: I
Do infinitely many pairs occur in Ulam's sequence?
Mathematical statement
Do infinitely many pairs occur in Ulam's sequence?
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_342.parts.i
Complete statement target, proof intentionally absentLean 4
theorem erdos_342.parts.i : answer(sorry) ↔ ∀ a : ℕ → ℕ, IsUlamSequence a → Set.Infinite {n : ℕ | ∃ m, a m = a n + 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