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arXiv · 2602.05732

$3n + 3^k$ Problem

David Barina·W. C. Maat
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Abstract

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 $3^k$.

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David Barina, W. C. Maat. 2026-02-05. $3n + 3^k$ Problem. https://doi.org/10.12921/cmst.2025.0000007

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