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 .
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页数：10
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