spectacular nerdularity

[rone]

There's a puzzle in KoTOR which looks like this:

What are the next two steps of this progression? 4, 14, 11-14, 31-14, 13-21-14.

It's enough to drive any math nerd insane.  The answers are 31-13-12-14 and 23-41-12-14.  The trick is to read the progression out loud: 4 is "one four", so you write down 14; then 14 is "one one, one four", 11-14; you read 11-14 as "three ones, one four", 31-14.  So, i got to thinking, "How far can you take this?"

1 11 21 12-11 31-12 13-21-12 31-13-22 23-21-22 42-13-11 14-12-31-13 41-14-12-23 24-31-22-13 32-14-23-21 23-32-21-14 32-23-21-14 (the last two repeat)

2 12 11-12 31-12 [etc.]

3 13 11-13 31-13 23-21 22-13-11 22-31-13 22-23-21 42-13-11 [etc.]

4 14 11-14 31-14 13-21-14 31-13-12-14 23-41-12-14 22-13-24-31 32-21-23-14 23-32-21-14 32-23-21-14 (the last two repeat)

For any other digit n, it's:

n
1n
11-1n
31-1n
13-21-1n
31-13-12-1n
23-41-12-1n
22-13-14-31-1n
22-41-23-14-1n
32-24-31-13-1n
33-22-14-31-1n
33-22-31-14-1n
(repeats)

So... what conclusions can we extract?  The words of Gregg Easterbrook's alter ego, Tuesday Morning Quarterback, come to mind:

This is the kind of hidden indicator that is essential to an insider's understanding of the game. Unfortunately, Tuesday Morning Quarterback has no idea what it means.