$v$-Palindromes: An Analogy to the Palindromes
| Autor: | Bispels, Chris, Boran, Muhammet, Miller, Steven J., Sosis, Eliel, Tsai, Daniel |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $198 = 2\cdot 3^2\cdot 11$ and $891 = 3^4\cdot 11$ 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 $p^2+1$, for each odd prime $p$. Finally, we collect some conjectures and problems involving $v$-palindromes. Comment: 22 pages, 2 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:2111.10211 |
| Databáze: | arXiv |
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