If you extrapolate the pattern a bit while focusing on a certain area, I think you can establish enough to get you to the solution.
For example, if you look at the numbers in the count where you are hitting the 'first finger', you get the following pattern:
2,8,10,16,18,24....
You can see that every second number here represents the eight-times-table.
So:
2,8,10,16,18,24....
(8x_) 1 2 3.....
Each odd multiple of eight corresponds to the sweep FROM little-finger TO thumb, and each even multiple of eight corresponds FROM thumb, TO little finger.
2013/8 = 251.625
251 * 8 = 2008
So the number 2008 hits the first finger, and as it is an ODD multiple of eight it hits the first finger whilst moving in the direction from little finger to thumb. Therefore,
2008: 1st finger
2009: Thumb
2010: 1st finger
2011: 2nd finger
2012: 3rd finger
2013: little finger.
I'm sure there are simpler or more elegant formulaic ways to establish this, but unless I'm mistaken this does the job.