On integrality and asymptotic behavior of the $(k,l)$-Göbel sequences

Recently, Matsuhira, Matsusaka, and Tsuchida revisited old studies on the integrality of $k$-Göbel sequences and showed that the first 19 terms are always integers for any integer $k\ge 2$. In this article, we further explore two topics: Ibstedt’s $(k,l)$-Göbel sequences and Zagier’s asymptotic formula for the $2$-Göbel sequence, and extend their results.