Antipalindromic numbers

Authors

  • Ľubomíra Dvořáková Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Trojanova 13, 120 00 Praha 2, Czech Republic
  • Stanislav Kruml Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics, Trojanova 13, 120 00 Praha 2, Czech Republic
  • David Ryzák Charles University, Faculty of Mathematics and Physics, Ke Karlovu 2027, 121 16 Praha 2, Czech Republic

DOI:

https://doi.org/10.14311/AP.2021.61.0428

Keywords:

Expansion in a base, palindromes, antipalindromes, palindromic numbers, 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, multi-base 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 multi-base antipalindromic numbers. We provide a user-friendly application for all studied questions.

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Published

2021-06-30

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Articles