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Erdős problem 317

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Is there some constant c>0c>0 such that for every n≥1n\geq 1 there exists some δk∈{−1,0,1}\delta_k\in \{-1,0,1\} for 1≤k≤n1\leq k\leq n with 0<∣∑1≤k≤nδkk∣<c2n?0< \left\lvert \sum_{1\leq k\leq n}\frac{\delta_k}{k}\right\rvert < \frac{c}{2^n}?

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The source's own material, retained exactly.

4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

317.lean

Retained formal statement1 of 4

Inequality in erdos_317.variants.claim2 is obvious, the problem is strict inequality.

FormalConjectures/ErdosProblems/317.leanErdos317.claim2_inequality3 linesExact file
∀ᶠ (n : ℕ) in Filter.atTop,  ∀ (δ : Fin n → ℚ),    δ '' Set.univ ⊆ {-1, 0, 1} → |∑ k, δ k / (↑↑k + 1)| ≠ 0 → |∑ k, δ k / (↑↑k + 1)| ≥ 1 / ↑((Finset.Icc 1 n).lcm id)
TextbookStatement only, no proof