A complete comparison for the number of palindromes in different bases-Reference-Cited by-同舟云学术

A complete comparison for the number of palindromes in different bases

Published:2023 Issue:4 Volume:8 Page:9924-9932
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Phunphayap Phakhinkon Napp¹,Pongsriiam Prapanpong²³

Affiliation:

1. Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

2. Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand

3. Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Abstract

<abstract><p>Let $ b $ and $ b_1 $ be distinct positive integers larger than $ 1 $, and let $ A_{b} (n) $ and $ A_{b_1} (n) $ be the number of palindromes in bases $ b $ and $ b_1 $ that are less than or equal to $ n $, respectively. In this article, we finish the comparative study of the functions $ A_b (n) $ and $ A_{b_1} (n) $. As a result, we present the full picture of the asymptotic behavior of their difference.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference17 articles.

1. P. Phunphayap, P. Pongsriiam, Extremal orders and races between palindromes in different bases, AIMS Math., 7 (2022), 2237–2254. https://doi.org/10.3934/math.2022127

2. W. D. Banks, D. N. Hart, M. Sakata, Almost all palindromes are composite, Math. Res. Lett., 11 (2004), 853–868. https://doi.org/10.4310/MRL.2004.v11.n6.a10

3. W. D. Banks, I. E. Shparlinski, Prime divisors of palindromes, Period. Math. Hung., 51 (2005), 1–10. https://doi.org/10.1007/s10998-005-0016-6

4. W. D. Banks, Every natural number is the sum of forty-nine palindromes, Integers, 16 (2016), 1–9.

5. J. Cilleruelo, F. Luca, L. Baxter, Every positive integer is a sum of three palindromes, Math. Comput., 87 (2018), 3023–3055. https://doi.org/10.1090/mcom/3221