Problem 950

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Statement. Let

$$f(n) = \sum_{p<n}\frac{1}{n-p}.$$

Is it true that

$$\liminf f(n)=1$$

and

$$\limsup f(n)=\infty?$$

Is it true that $f(n)=o(\log\log n)$ for all $n$?

Status. Open.

Source. erdosproblems.com/950, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #950, https://www.erdosproblems.com/950.

Formalization. Statement in formal-conjectures.

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