The Steinhaus Cyclus

The Steinhaus Cyclus is 145, 42, 20, 4, 16, 37, 58, 89.

1. Take any natural number with 4 digits. (abcd)
2. Add the squares of the digits. (a²+b²+c²+d²)
3. Handle this sum in the same way. Repeat this calculation.
4. This procedure comes either to 1 or inevitably to number 145. 
5. Then the cyclus 42, 20, 4, 16, 37, 58, 89, 145 repeats.

1st example:

• Take the number 4363.
• Sequence: 70, 49, 97, 130, 10, 1, 1, 1, 1,...

2nd example:

• Take the number 9583.
• Sequence: 179, 131, 11, 2, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, 145, 42, 20, 4, 16, 37, 58, 89, ...

See http://www.mathematische-basteleien.de/kaprekar.htm#The%20number%20222