Source labels openChecked July 26, 2026

Erdős Problem 260

Let $a_1 < a_2 < \cdots$ be an increasing sequence such that $\frac{a_n}{n} \to \infty$ . Is the sum $\sum_{n}^{\infty} \frac{a_n}{2^{a_n}}$ irrational?

Number theory AMS 11

Mathematical statement

Let $a_1 < a_2 < \cdots$ be an increasing sequence such that $\frac{a_n}{n} \to \infty$ . Is the sum $\sum_{n}^{\infty} \frac{a_n}{2^{a_n}}$ irrational?

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_260

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_260 : answer(sorry) ↔                  ∀ a : ℕ → ℤ, ∀ s : ℝ,                  StrictMono a →                  Tendsto (fun n => (a n : ℝ ) / n ) atTop atTop →                  HasSum (fun n => (a n : ℝ ) / 2 ^ a n) s → Irrational s :=  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/260background