Harry, now that you published the solution, I had a totally different method of going about the sequence problem. Here is is again:
3,3,10,11,11,18,10,10,17, …
I noticed that 11-3=8 and 10+8=18. Furthermore, 10-11=-1 and 18+-1 is 17. Also, I noticed that the doubled ten followed on from a single ten. So I reasoned that the next doubled number would be 18. Carrying this pattern on, I got 18-10=8. 8+17=25. Therefore, the next terms of the sequence are 18,18,25…
More than one way to crack a nut!