Aperiodvent, Day 11: Lychrel numbers

Many numbers, if you repeatedly add them to the number formed by reversing their own digits, will eventually lead to a palindrome. For example:

\begin{align}
7326 + 6237 &= 13563 \\
13563 + 36531 &= 50094 \\
50094 + 49005 &= 99099
\end{align}

For most numbers, this happens with in fewer than 10 iterations. However, Wade in Florida has discovered that some numbers – including 196 – seem to never reach a palindrome. At latest update, they’ve tried over a billion iterations on 196, and no sign of a palindrome yet. These types of number, which don’t seem to become palindromes (as yet unproven, as far as I can tell, but work continues) are named after Wade’s wife, and are called Lychrel numbers.

To find out more, and see many examples he’s found, visit Wade’s website at p196.org.

This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!

About the author

• Katie Steckles

Publicly engaging mathematician, Manchester MathsJam organiser, hairdo.