On the order of magnitude of certain integer sequences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917689096667136 |
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| author | Hellus, Michael Rechenauer, Anton Waldi, Rolf |
| author_facet | Hellus, Michael Rechenauer, Anton Waldi, Rolf |
| contents | Let $p$ be a prime number, and let $S$ be the numerical semigroup generated by the prime numbers not less than $p$. We compare the orders of magnitude of some invariants of $S$ with each other, e. g., the biggest atom $u$ of $S$ with $p$ itself: By Harald Helfgott (arXiv:1312.7748 [math.NT]), every odd integer $N$ greater than five can be written as the sum of three prime numbers. There is numerical evidence suggesting that the summands of $N$ always can be chosen between $\frac N6$ and $\frac N2$. This would imply that $u$ is less than $6p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the order of magnitude of certain integer sequences Hellus, Michael Rechenauer, Anton Waldi, Rolf Number Theory 11D07 (Primary) 20M14 (Secondary) Let $p$ be a prime number, and let $S$ be the numerical semigroup generated by the prime numbers not less than $p$. We compare the orders of magnitude of some invariants of $S$ with each other, e. g., the biggest atom $u$ of $S$ with $p$ itself: By Harald Helfgott (arXiv:1312.7748 [math.NT]), every odd integer $N$ greater than five can be written as the sum of three prime numbers. There is numerical evidence suggesting that the summands of $N$ always can be chosen between $\frac N6$ and $\frac N2$. This would imply that $u$ is less than $6p$. |
| title | On the order of magnitude of certain integer sequences |
| topic | Number Theory 11D07 (Primary) 20M14 (Secondary) |
| url | https://arxiv.org/abs/2404.14765 |