2021/11/17 by Tsai, Daniel
#11A51 #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO) #Primary 11A63 #Secondary 11A25
paper · doi:10.48550/arxiv.2111.10211
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.