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arXiv · 1207.7059

On a sequence involving sums of primes

Zhi-Wei Sun
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Abstract

For $n=1,2,3,\ldots$ let $S_n$ be the sum of the first $n$ primes. We mainly show that the sequence $a_n=\root n\of{S_n/n}\ (n=1,2,3,\ldots)$ is strictly decreasing, and moreover the sequence $a_{n+1}/a_n\ (n=10,11,\ldots)$ is strictly increasing. We also formulate similar conjectures involving twin primes or partitions of integers.

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Zhi-Wei Sun. 2013-10-31. On a sequence involving sums of primes. https://arxiv.org/abs/1207.7059

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