The characteristic sequence of the integers that are the sum of two squares is not morphic
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909169068539904 |
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| author | Li, Shuo |
| author_facet | Li, Shuo |
| contents | Let $(s_2(n))_{n\in \mathbb{N}}$ be a $0,1$-sequence such that, for any natural number $n$, $s_2(n) = 1$ if and only if $n$ is a sum of two squares. In a recent article, Tahay proved that the sequence $(s_2(n))_{n\in \mathbb{N}}$ is not $k$-automatic for any integer $k$, and asked if this sequence can be morphic. In this note, we give a negative answer to this question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08822 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The characteristic sequence of the integers that are the sum of two squares is not morphic Li, Shuo Number Theory Combinatorics Let $(s_2(n))_{n\in \mathbb{N}}$ be a $0,1$-sequence such that, for any natural number $n$, $s_2(n) = 1$ if and only if $n$ is a sum of two squares. In a recent article, Tahay proved that the sequence $(s_2(n))_{n\in \mathbb{N}}$ is not $k$-automatic for any integer $k$, and asked if this sequence can be morphic. In this note, we give a negative answer to this question. |
| title | The characteristic sequence of the integers that are the sum of two squares is not morphic |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2404.08822 |