International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 2999-3004

Searching for Kaprekar's constants: algorithms and results

Byron L. Walden

Department of Mathematics and Computer Science, Santa Clara University, Santa Clara 95053-0290, CA, USA

Received 7 April 2004

Copyright © 2005 Byron L. Walden. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We examine some new results on Kaprekar's constants, specifically establishing the unique 7-digit (in base 4) and 9-digit (in base 5) Kaprekar's constants and showing that there are no 15-, 21-, 27-, or 33-digit Kaprekar's constants.