Pattern:1,2,10,11,12,20,21,22,100,…
Last number in the sequence: 3^5, or 100,000 in base 3.
In this sequence, every third number has a zero, and every 9th number has 2 zeros, and so on.
If we add all of these together, we will get: 81+27+9+3+1=121 zeros.
Hope this helped!