Source labels openChecked July 26, 2026

Erdős Problem 247

Let $n_1 < n_2 < \cdots$ be a sequence of integers such that $\limsup \frac{n_k}{k} = \infty.$ Is $\sum_{k=1}^{\infty} \frac{1}{2^{n_k}}$ transcendental?

Number theory AMS 11

Mathematical statement

Let $n_1 < n_2 < \cdots$ be a sequence of integers such that

\limsup \frac{n_k}{k} = \infty.

\sum_{k=1}^{\infty} \frac{1}{2^{n_k}}

transcendental?

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_247

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_247 : answer(sorry) ↔ ∀ (n : ℕ → ℕ), (StrictMono n) →    atTop.limsup (fun k => (n k / k.succ : EReal)) = ⊤ →    Transcendental ℚ (∑' k, (1 : ℝ) / 2 ^ n k) := 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/247background