English

On integrality and asymptotic behavior of the $(k, l)$-G\"{o}bel sequences

Number Theory 2024-02-15 v1

Abstract

Recently, Matsuhira, Matsusaka, and Tsuchida revisited old studies on the integrality of kk-G\"{o}bel sequences and showed that the first 19 terms are always integers for any integer k2k\ge 2. In this article, we further explore two topics: Ibstedt's (k,l)(k,l)-G\"{o}bel sequences and Zagier's asymptotic formula for the 22-G\"{o}bel sequence, and extend their results.

Keywords

Cite

@article{arxiv.2402.09064,
  title  = {On integrality and asymptotic behavior of the $(k, l)$-G\"{o}bel sequences},
  author = {Hibiki Gima and Toshiki Matsusaka and Taichi Miyazaki and Shunta Yara},
  journal= {arXiv preprint arXiv:2402.09064},
  year   = {2024}
}

Comments

10 pages