Elementary Proof of the Completeness of OEIS A051221 Below 2000
Number Theory
2025-04-02 v1
Abstract
The OEIS sequence A051221 consists of nonnegative integers of the form 10^x - y^2. The known values are those less than or equal to 2000 with x <= 7, and it is conjectured that no new values in this range appear for x >= 8. In this paper, we give an elementary proof that this is indeed the case by using Pell-type equations.
Cite
@article{arxiv.2504.00116,
title = {Elementary Proof of the Completeness of OEIS A051221 Below 2000},
author = {Seiichi Azuma},
journal= {arXiv preprint arXiv:2504.00116},
year = {2025}
}
Comments
5 pages, no figures. Related OEIS sequence: A051221. Colab notebook available at https://colab.research.google.com/drive/1c77O20BIBMl_UMuH4MmnhKy0POM9LBc-? usp=sharing