TL;DR
This paper introduces and investigates antipalindromic numbers, exploring their properties, divisibility, primes, powers, and multibased forms, along with a user-friendly application for these concepts.
Contribution
It defines antipalindromic numbers and presents new results on their divisibility, prime status, powers, and multibased representations, expanding the study of number palindromes.
Findings
New divisibility properties for antipalindromic numbers
Characterization of antipalindromic primes and powers
Development of a user-friendly application for studying antipalindromic numbers
Abstract
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.
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