Fingering for Oscar Peterson Jazz Exercise #2 in G

Question

I'm primarily concerned with the run at the end of the 2nd measure, but fingerings before that would also help. Below are the three measures of interest.

Edit: Added the next (3rd) measure as pointed out in an answer.

Answer 1

Any set of fingering is affected by other characters of the music in question. In what tempo is it? How free is it? Is legato desired? And what follows the last note C#? Nevertheless, I might use

4 5 4 1 2 3 4 5 4
          1 1 2 3

If you are not used to this, or the tempo is really fast, then you might consider

4 5 4 1 2 2 3 4 5
          1 1 2 3

What do you think? play on the keyboard and comment, good luck!

Answer 2

The OP missed one important fact from the question: what comes after those four double-thirds? The answer is another third on B/D, followed by a top G.

Considering that, and also the fact that there is no sense in trying to play this perfectly legato anyway, I would go for something like

4 5 4 2 1 

(you don't want to tie yourself in a knot by putting your thumb on the F#, but if you do something like 3 4 3 1 2 followed by 3-5 you have run out of fingers for the rest of the thirds)

then

3 4 3 4
2 1 1 2

for the thirds

and

3 5 
1

to start the next bar.

That fingering for the thirds might seem weird, but start by practicing some ordinary scales with the fingering 3 4 3 4 3 4 3 4... or 2 3 2 3 2 3 2 3 to get used to the general idea. (Fun piece of trivia: that was how all keyboard scales were fingered when keyboard instruments were first invented, over 400 years ago - this isn't some "new technique for playing jazz"!)