Cloitre's Self-Generating Sequence
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909446398017536 |
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| author | Shallit, Jeffrey |
| author_facet | Shallit, Jeffrey |
| contents | In 2009 Benoit Cloitre introduced a certain self-generating sequence $$(a_n)_{n\geq 1} = 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, \ldots,$$ with the property that the sum of the terms appearing in the $n$'th run equals twice the $n$'th term of the sequence. We give a connection between this sequence and the paperfolding sequence, and then prove Cloitre's conjecture about the density of $1$'s appearing in $(a_n)_{n \geq 1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cloitre's Self-Generating Sequence Shallit, Jeffrey Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory In 2009 Benoit Cloitre introduced a certain self-generating sequence $$(a_n)_{n\geq 1} = 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, \ldots,$$ with the property that the sum of the terms appearing in the $n$'th run equals twice the $n$'th term of the sequence. We give a connection between this sequence and the paperfolding sequence, and then prove Cloitre's conjecture about the density of $1$'s appearing in $(a_n)_{n \geq 1}$. |
| title | Cloitre's Self-Generating Sequence |
| topic | Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory |
| url | https://arxiv.org/abs/2501.00784 |