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