These chords progress in units of 2. So you start with your triad (1st, 3rd, 5th). For the 7th chord you add the 7th, naturally enough. The next chord is then a 9th chord, so you add a 9th interval, but it wraps around modulo 8, so it's really a 2nd interval (since intervals are 1-indexed). Next it's an 11th chord, but the interval is really a 4th, and so on. The idea is to think of them spread out though, as successive thirds.
In what's typically called a 13th chord, the 11th is almost always omitted because it either clashes, or it changes the chord into something completely different. Stacking 3rds doesn't actually explain how jazz chords work. And it tends to produce corny voicings.
To make an analogy with computers, it feels like the classical notation is an abstraction layer which has been extended beyond its usefulness.
