Why are 1/3 stop apertures uneven numbers apart?

Why do 1/3 stop apertures go like 8, 9, 10, 11, 13, 14, 16, 18?

There's a difference of 2 between 11 and 13, it goes back to 1 between 13 and 14, and it goes back up to 2.

Answer

For f/stops, there is a precise multiplied difference of 1.122462 X intervals (cube root of √2) between all third stops. The precise third stops are actually numbers like 8.98 or 10.08. My meaning of the Precise Numbers is of course the theoretical precise goal numbers that the camera designer certainly aims for. There can be no question about those (even if the physical camera mechanisms may not necessarily be precisely accurate to as many decimal places). But the nominal numbers that are marked and shown are arbitrarily rounded to numbers like 9 or 10, but the camera and lens design tries to actually compute with the actual precise values.

Precise Nominal Stop
8       8       Full
8.98    9       ⅓
10.08   10      ⅔

11.31   11      Full
12.7    13      ⅓
14.25   14      ⅔
16      16      Full

The same concept (of there being precise and nominal values) is true of f/stops, shutter speeds, and ISO. For shutter speed and ISO, then thirds are 1.259921 X intervals (∛2).

These are valid results, but not the fundamental definition, and complete detail is shown at my site at https://www.scantips.com/lights/fstop2.html