Example rules

Standard

Double the number and add two; eg 12 -> 26

Write the number in reverse; eg 13 -> 31

Write the number twice; eg 42 -> 4242

Count the number of characters in the word for the number; eg 21 -> 10

Advanced

The number of the number's prime factors; eg 15 -> 2

The sum of the squares of the number's digits; eg 13 -> 10

The number written in base three; eg 26 -> 222