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v-palindromes: an analogy to the palindromes

Name: v-palindromes: an analogy to the palindromes
Creator: Tsai, Daniel
Keywords: Mathematics - History and Overview, History and Overview (math.HO), FOS: Mathematics, Primary 11A63, Secondary 11A25, 11A51, Mathematics - Combinatorics, Combinatorics (math.CO)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2021Embargo end date: 01 Jan 2021Publisher:arXiv

Authors: Tsai, Daniel;

doi: 10.48550/arxiv.2111.10211

arXiv: http://arxiv.org/abs/2111.10211

v-palindromes: an analogy to the palindromes

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Abstract

In the year 2007, the author discovered an intriguing property of the number $198$ he saw on the license plate of a car. Namely, if we take $198$ and its reversal $891$, prime factorize each number, and sum the numbers appearing in each factorization, both sums are $18$. Such numbers are formally introduced in a short published note in 2018. These numbers are 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. Finally, we collect some conjectures on $v$-palindromes.

9 pages, 1 table

Keywords

Mathematics - History and Overview, History and Overview (math.HO), FOS: Mathematics, Primary 11A63, Secondary 11A25, 11A51, Mathematics - Combinatorics, Combinatorics (math.CO)

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