On the length over which k-G\"obel sequences remain integers

Q: What type of study is this?

This is a Quantitative Study study.

Yuji Kobayashi; Shin-ichiro Seki

doi:10.48550/arxiv.2502.17448

February 5, 2025Open Access

On the length over which k-G\"obel sequences remain integers

View Full Paper

Ask AI

Bookmark

Share

Key Points

The sequence of smallest positive integers for k-G"obel terms is shown to be unbounded.
As k increases, the integers in the k-G"obel sequence increasingly do not remain as integers.
The proof establishes the infinite nature of gaps within the sequence of k-G"obel terms.
This result highlights important properties of integer sequences and their variability.

Implication

The sequence of smallest integers for k-G"obel terms is unbounded, indicating a significant gap in integer values.

Abstract

We prove that the sequence (Nₖ)ₖ, where each Nₖ is defined as the smallest positive integer n for which the nth term gk,n of the k-G\"obel sequence is not an integer, is unbounded.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Kobayashi et al. (2025) studied this question.

synapsesocial.com/papers/68f0d5eb105731330a2b1ed7 https://doi.org/10.48550/arxiv.2502.17448

View Full Paper

Ask AI

Bookmark

Share

On the length over which k-G\"obel sequences remain integers

Key Points

Implication

Abstract

Discussion

Cite This Study

On the length over which k-G\"obel sequences remain integers

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

More related papers

Keep reading

More related papers