On the intimate association between even binary palindromic words and the Collatz-Hailstone iterations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917739434606592 |
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| author | Raptis, T. |
| author_facet | Raptis, T. |
| contents | The celebrated $3x+1$ problem is reformulated via the use of an analytic expression of the trailing zeros sequence resulting in a single branch formula $f(x)+1$ with a unique fixed point. The resultant formula $f(x)$ is also found to coincide with that of the discrete derivative of the sorted sequence of fixed points of the reflection operator on even binary palindromes of fixed even length \textit{2k} in any interval $[0\cdots2^{2k}-1]$. A set of equivalent reformulations of the problem are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the intimate association between even binary palindromic words and the Collatz-Hailstone iterations Raptis, T. General Mathematics The celebrated $3x+1$ problem is reformulated via the use of an analytic expression of the trailing zeros sequence resulting in a single branch formula $f(x)+1$ with a unique fixed point. The resultant formula $f(x)$ is also found to coincide with that of the discrete derivative of the sorted sequence of fixed points of the reflection operator on even binary palindromes of fixed even length \textit{2k} in any interval $[0\cdots2^{2k}-1]$. A set of equivalent reformulations of the problem are also presented. |
| title | On the intimate association between even binary palindromic words and the Collatz-Hailstone iterations |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2408.00805 |