Erdős problem 480 · problems.science

Let $x_1,x_2,\ldots\in [0,1]$ be an infinite sequence. Is it true that $\inf_n \liminf_{m\to \infty} n \lvert x_{m+n}-x_m\rvert\leq 5^{-1/2}\approx 0.447?$ A conjecture of Newman.

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480.lean

Retained formal statement1 of 3

Let $x_1,x_2,\ldots\in [0,1]$ be an infinite sequence. Is it true that $\inf_n \liminf_{m\to \infty} n \lvert x_{m+n}-x_m\rvert\leq 5^{-1/2}\approx 0.447?$ A conjecture of Newman.

FormalConjectures/ErdosProblems/480.leanErdos480.erdos_4803 linesExact file

1True ↔2  ∀ (x : ℕ → ℝ),3    (∀ (n : ℕ), x n ∈ Set.Icc 0 1) → ⨅ n, Filter.liminf (fun m => ↑↑n * |x (m + ↑n) - x m|) Filter.atTop ≤ 1 / √5

SolvedStatement only, no proof

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