How Long Can k-Gobel Sequences Remain Integers?

被引：0

作者：

Matsuhira, Rinnosuke ^{[1
]}

Matsusaka, Toshiki ^{[2
]}

Tsuchida, Koki ^{[1
]}

机构：

[1] Kyushu Univ, Dept Math, Motooka 744,Nishi ku, Fukuoka 8190395, Japan

[2] Kyushu Univ, Fac Math, Motooka 744,Nishi ku, Fukuoka 8190395, Japan

来源：

AMERICAN MATHEMATICAL MONTHLY | 2024年

关键词：

D O I：

10.1080/00029890.2024.2379748

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Inspired by Episode 3 of the Japanese manga "Seisu-tan" by Doom Kobayashi and Shin-ichiro Seki, we investigate the k-Gobel sequence (g(k,n))(n) named after Fritz Gobel. 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 gk,n is always an integer for any k >= 2 and 0 <= n <= 18 .

引用

页数：10

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