I can across an exotic number system known as a sandpile on Numberphile video.

Exploiting Julia fantastic type system and very cool index handling, I put implements that sandpile addition operator demonstrated in the Numberphile video.

The notebook can be found here.

I was recently introduced to Kaperkar’s Constant.
It is quite magical. You take any four digit number \(A\), sort the digits from highest to lowest to create a new number \(A^{\text{high}}\), sort the digits from lowest to highest to get \(A^{\text{low}}\), and calculate and new number \(A= A^{\text{high}}- A^{\text{low}}\). You repeat this procedure enough times and you end up with \(A=6174\).

I made a nifty implementation of that in Julia below.

https://gist.github.com/mbeltagy/b27f5cc93346d5e0614c92ab696dfc31