Completeness of exponentially increasing sequences
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911472835100672 |
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| author | van Doorn, Wouter |
| author_facet | van Doorn, Wouter |
| contents | For fixed positive reals $t$ and $α$, consider the sequence $S_t(α) = (s_1, s_2, \ldots, )$ with $s_n = \left \lfloor tα^n \right \rfloor$. In 1964, Graham managed to characterize those pairs $(t, α)$ with $0 < t < 1$ and $1 < α< 2$ for which every large enough integer can be written as the sum of distinct elements of $S_t(α)$. We show that his methods can be applied to deal with many other pairs of $(t, α)$ as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23394 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Completeness of exponentially increasing sequences van Doorn, Wouter Number Theory For fixed positive reals $t$ and $α$, consider the sequence $S_t(α) = (s_1, s_2, \ldots, )$ with $s_n = \left \lfloor tα^n \right \rfloor$. In 1964, Graham managed to characterize those pairs $(t, α)$ with $0 < t < 1$ and $1 < α< 2$ for which every large enough integer can be written as the sum of distinct elements of $S_t(α)$. We show that his methods can be applied to deal with many other pairs of $(t, α)$ as well. |
| title | Completeness of exponentially increasing sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.23394 |