How long can $k$-Göbel sequences remain integers?

Rinnosuke Matsuhira, Toshiki Matsusaka, Koki Tsuchida

Inspired by Episode 3 of the Japanese manga "Seisu-tan" by Doom Kobayashi and Shin-ichiro Seki, we investigate the $k$-Göbel sequence $(g_{k,n}{)}_n$ named after Fritz Göbel. Althoug…