Ulam numbers have zero density
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910046605017088 |
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| author | Agama, Theophilus |
| author_facet | Agama, Theophilus |
| contents | In this paper, we show that the natural density $\mathcal{D}[(U_m)]$ of Ulam numbers $(U_m)$ satisfies $\mathcal{D}[(U_m)]=0$. That is, we show that for $(U_m)\subset [1,k]$ \begin{align} \lim \limits_{k\longrightarrow \infty}\frac{\left |(U_m)\cap [1,k]\right |}{k}=0.\nonumber \end{align} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_02697 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Ulam numbers have zero density Agama, Theophilus Number Theory In this paper, we show that the natural density $\mathcal{D}[(U_m)]$ of Ulam numbers $(U_m)$ satisfies $\mathcal{D}[(U_m)]=0$. That is, we show that for $(U_m)\subset [1,k]$ \begin{align} \lim \limits_{k\longrightarrow \infty}\frac{\left |(U_m)\cap [1,k]\right |}{k}=0.\nonumber \end{align} |
| title | Ulam numbers have zero density |
| topic | Number Theory |
| url | https://arxiv.org/abs/2007.02697 |