@article{Phunphayap2022, 
author = {Phakhinkon Phunphayap and Prapanpong Pongsriiam},
title = {Extremal orders and races between palindromes in different bases},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {2237-2254},
keywords = {palindrome, palindromic number, extremal order, b-adic expansion, minimal order, maximal order},
url = {https://www.sciopen.com/article/10.3934/math.2022127},
doi = {10.3934/math.2022127},
abstract = {Let    b  ≥  2 and    n  ≥  1 be integers. Then    n is said to be a palindrome in base    b (or    b-adic palindrome) if the representation of    n in base    b reads the same backward as forward. Let        A    b    (  n  ) be the number of    b-adic palindromes less than or equal to    n. In this article, we obtain extremal orders of        A    b    (  n  ). We also study the comparison between the number of palindromes in different bases and prove that if    b  ≠      b          1      , then        A          b        (  n  )  −      A                  b                  1                      (  n  ) changes signs infinitely often as    n  →  ∞.}
}