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.
Citation: Phakhinkon Napp Phunphayap, Prapanpong Pongsriiam. A complete comparison for the number of palindromes in different bases[J]. AIMS Mathematics, 2023, 8(4): 9924-9932. doi: 10.3934/math.2023502
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.
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Phakhinkon Napp Phunphayap, Prapanpong Pongsriiam. A complete comparison for the number of palindromes in different bases[J]. AIMS Mathematics, 2023, 8(4): 9924-9932. doi: 10.3934/math.2023502
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