v-Palindromes: An Analogy to the Palindromes

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dc.contributor.authorBispels, Chris
dc.contributor.authorBoran, Muhammet
dc.contributor.authorMiller, Steven J.
dc.contributor.authorSosis, Eliel
dc.contributor.authorTsai, Daniel
dc.date.accessioned2024-06-11T13:30:18Z
dc.date.available2024-06-11T13:30:18Z
dc.date.issued2024-04-24
dc.description.abstractAround 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.
dc.description.urihttp://arxiv.org/abs/2405.05267
dc.format.extent22 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifierdoi:10.13016/m2tyrr-tju9
dc.identifier.urihttps://doi.org/10.48550/arXiv.2405.05267
dc.identifier.urihttp://hdl.handle.net/11603/34593
dc.language.isoen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.rightsCC BY 4.0 DEED Attribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject(Primary) 11A63, (Secondary) 11A25, 11A51
dc.subjectMathematics - History and Overview
dc.subjectMathematics - Number Theory
dc.titlev-Palindromes: An Analogy to the Palindromes
dc.typeText

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