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The PUMP Journal of Undergraduate Research
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v-Palindromes: an Analogy to the Palindromes

\(v\)-palindromes: an analogy to the palindromes
Authors: Bispels, Chris; Boran, Muhammet; Miller, Steven J.; Sosis, Eliel; Tsai, Daniel;

v-Palindromes: an Analogy to the Palindromes

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.

Keywords

primes, Mathematics - Number Theory, (Primary) 11A63, (Secondary) 11A25, 11A51, History and Overview (math.HO), Mathematics - History and Overview, Arithmetic functions; related numbers; inversion formulas, \(v\)-palindromes, FOS: Mathematics, Number Theory (math.NT), Factorization; primality, Radix representation; digital problems

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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