11, 12, 20, 23, 33, 46, ?, ?

Oops, sorry, messed up my bases there.  

Haven't read the other posts, so this may be redundant.

The numbers are Fibonacci numbers starting with 3 in base 2, then 5 in base 3, 8 in base 4, 13 in base 5, 21 in base 6, and 34 in base 7.  The next 2 numbers are:

67   (55 in base 8)
98   (89 in base 9)

As far as the philosophy of what makes the best answer (now I have read the other posts), I think there should be something akin to esthetic points for "cleverness" or "uniqueness of ideas".  So for this series combining Fib with a changing base seems to me to be "better" than, say, a "kicked up a notch" geometric series.  But then that's just me.  Then again, sometimes I mess up translating bases.