This appears to be two interleaved series. The first is

2 5 10 17 (26) (37) ...

It has first differences that increase by 2 each time,

3 5 7 (9) (11) ...

The second series is

9 13 19 (27) (37) ...

It also has first differences that increase by 2 each time,

4 6 (8) (10) ...

The next four numbers of your series appear to be

... 27 26 37 37

2 5 10 17 (26) (37) ...

It has first differences that increase by 2 each time,

3 5 7 (9) (11) ...

The second series is

9 13 19 (27) (37) ...

It also has first differences that increase by 2 each time,

4 6 (8) (10) ...

The next four numbers of your series appear to be

... 27 26 37 37