2020/08/16 by Dvorakova, Lubomira, Kruml, Stanislav, Ryzak, David
#68R15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.06864
Everybody has certainly heard about palindromes: words that stay the same when read backwards. For instance kayak, radar, or rotor. Mathematicians are interested in palindromic numbers: positive integers whose expansion in a certain integer base is a palindrome. The following problems are studied: palindromic primes, palindromic squares and higher powers, multibased palindromic numbers, etc. In this paper, we define and study antipalindromic numbers: positive integers whose expansion in a certain integer base is an antipalindrome. We present new results concerning divisibility and antipalindromic primes, antipalindromic squares and higher powers, and multibased antipalindromic numbers. We provide a user-friendly application for all studied questions.