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arXiv · 2307.09741

How long can $k$-G\"{o}bel sequences remain integers?

Rinnosuke Matsuhira·Toshiki Matsusaka·Koki Tsuchida
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Abstract

Inspired by Episode 3 of the Japanese manga "Seisu-tan" by Doom Kobayashi and Shin-ichiro Seki, we investigate the $k$-G\"{o}bel sequence $(g_{k,n})_n$ named after Fritz G\"{o}bel. Although the sequence is generally defined as rational, quite a few initial terms behave like an integer sequence. This article addresses a question raised in Seisu-tan and shows that $g_{k,n}$ is always an integer for any $k \geq 2$ and $0 \leq n \leq 18$.

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Rinnosuke Matsuhira, Toshiki Matsusaka, Koki Tsuchida. 2023-07-19. How long can $k$-G\"{o}bel sequences remain integers?. https://doi.org/10.1080/00029890.2024.2379748

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