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arXiv · 2502.17448

On the length over which $k$-Göbel sequences remain integers

Yuh Kobayashi·Shin-ichiro Seki
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Abstract

We prove that the sequence $(N_k)_k$, where each $N_k$ is defined as the smallest positive integer $n$ for which the $n$th term $g_{k,n}$ of the $k$-Göbel sequence is not an integer, is unbounded.

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Yuh Kobayashi, Shin-ichiro Seki. 2025-02-05. On the length over which $k$-Göbel sequences remain integers. https://arxiv.org/abs/2502.17448

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