$3n + 3^k$ Problem
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911424537690112 |
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| author | Barina, David Maat, W. C. |
| author_facet | Barina, David Maat, W. C. |
| contents | The Collatz problem is generalized into $3n + 3^k$ problem. It is shown that as long as the Collatz function iterates converge to the cycle passing through the number 1, the $3n + 3^k$ sequence converges to the cycle passing through the number $3^k$ for arbitrary positive integers $n$ and $k$. The proof shows that the sequence of $3n + 3^k$ function iterates for a number $3^k n$ is exactly the sequence of the Collatz function iterates for $n$ multiplied by $3^k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $3n + 3^k$ Problem Barina, David Maat, W. C. General Mathematics The Collatz problem is generalized into $3n + 3^k$ problem. It is shown that as long as the Collatz function iterates converge to the cycle passing through the number 1, the $3n + 3^k$ sequence converges to the cycle passing through the number $3^k$ for arbitrary positive integers $n$ and $k$. The proof shows that the sequence of $3n + 3^k$ function iterates for a number $3^k n$ is exactly the sequence of the Collatz function iterates for $n$ multiplied by $3^k$. |
| title | $3n + 3^k$ Problem |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2602.05732 |