Rubik's Cube Orders Table

Here's the idea behind this: starting from the starting sequence, any sequence of moves will eventually bring you back there when performed enough times. The 'order' of a move sequence is the smallest positive integer n such that, starting with a solved cube, performing that move sequence n times will bring you back to the solved state. This page is a table of the shortest known (by me) sequences that have specific orders. A cell is left blank if I don't know any sequence with that order, and I only listed the rows for which I know at least one sequence on one of the cubes.

Before you begin, you might want to read up on the normal cubing notation. I'm using a lowercase letter (such as r) to mean a double-layer move, and an uppercase letter with a number in front (such as 2R) to mean a move of the 2nd layer on the R side.

I generated most of this table with a computer program that searched through all sequences of a certain length; I checked all 2x2 and 3x3 sequences of up to 5 moves, and all 4x4 sequences of up to 4 moves. It's possible that I may have missed some orders, though. If you have anything to add (or can improve on the length of some of these sequences), please let me know.