v-Palindromes: An Analogy to the Palindromes

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2405.05267v1.pdf (281.17 KB)

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http://arxiv.org/abs/2405.05267

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https://doi.org/10.48550/arXiv.2405.05267
 http://hdl.handle.net/11603/34593

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UMBC Student Collection
UMBC Mathematics and Statistics Department

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Date

2024-04-24

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journal articles
preprints
Text

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Citation of Original Publication

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CC BY 4.0 DEED Attribution 4.0 International

Subjects

(Primary) 11A63, (Secondary) 11A25, 11A51
Mathematics - History and Overview
Mathematics - Number Theory

Abstract

Around the year 2007, one of the authors, Tsai, accidentally discovered a property of the number 198 he saw on the license plate of a car. Namely, if we take 198 and its reversal 891, which have prime factorizations 198 = 2 · 3² · 11 and 891 = 3⁴ · 11 respectively, and sum the numbers appearing in each factorization getting 2 + 3 + 2 + 11 = 18 and 3 + 4 + 11 = 18, both sums are 18. Such numbers were later named v-palindromes because they can be viewed as an analogy to the usual palindromes. In this article, we introduce the concept of a v-palindrome in base b and prove their existence for infinitely many bases. We also exhibit infinite families of v-palindromes in bases p + 1 and p² + 1, for each odd prime p. Finally, we collect some conjectures and problems involving v-palindromes.