2024/04/24 by Bispels, Chris, Boran, Muhammet, Miller, Steven J. +2
#(Primary) 11A63 #(Secondary) 11A25 #11A51 #FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2405.05267
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.