erdos_377.variants.limit.i

Erdos, Graham, Ruzsa, and Straus proved that if $$ f(n) = \sum_{p \leq n} 1_{p\nmid {2n \choose n}}\frac{1}{p} $$ and $$ \gamma_0 = \sum_{k = 2}^{\infty} \frac{\log k}{2^k} $$ then $$ \lim_{x\to\infty} \frac{1}{x}\sum_{n\leq x} f(n) = \gamma_0 $$ [EGRS75] Erdős, P. and Graham, R. L. and Ruzsa, I. Z. and Straus, E. G., _On the prime factors of $\binom{2n}{n}$_. Math. Comp. (1975), 83-92.

theorem erdos_377.variants.limit.i (γ₀ : ℝ)
    (hγ₀ : γ₀ = ∑' (k : ℕ), (k + 2 : ℝ).log / 2 ^ (k + 2)) :
    Tendsto (fun (x : ℕ) => (1 : ℝ) / x * ∑ n ∈ Finset.Icc 1 x, sumInvPrimesNotDvdCentralBinom n)
      atTop (𝓝 γ₀)

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