Permalink Submitted by Michael Greaney on October 29, 2017

I can't help you with any literature, but I was intrigued by your observation that the repeated subtraction of a number from the absolute value of its reverse produced a palindrome.

I wrote a computer program to explore this and found that all numbers up to 10,002 become palindromes. The first number that doesn't result in a palindrome is 10,003. By not producing a palindrome I mean that doesn't produce one by the time the difference reaches a certain value, 9,223,372,036,854,775,807 in my case.

The program calculated

difference = number - absolute value(reverse)

using the difference as the new number.

The program repeated the calculation until the difference either became a palindrome or reached 9,223,372,036,854,775,807. A palindrome might result if this number were larger, but it might not. It's very much like Lychrel numbers in that regard.

## Emergent palindromes

I can't help you with any literature, but I was intrigued by your observation that the repeated subtraction of a number from the absolute value of its reverse produced a palindrome.

I wrote a computer program to explore this and found that all numbers up to 10,002 become palindromes. The first number that doesn't result in a palindrome is 10,003. By not producing a palindrome I mean that doesn't produce one by the time the difference reaches a certain value, 9,223,372,036,854,775,807 in my case.

The program calculated

difference = number - absolute value(reverse)

using the difference as the new number.

The program repeated the calculation until the difference either became a palindrome or reached 9,223,372,036,854,775,807. A palindrome might result if this number were larger, but it might not. It's very much like Lychrel numbers in that regard.