[seqfan] Cumulative sum of the digits used so far

[Eric Angelini]

Hello SeqFans,
I think this is the beginning of the 
slowest ever-increasing sequence
where a(n) is the sum of the digits 
present so far in the sequence, 
including the digits of a(n):

9, 18, 27, 36, 45, 54, 63, 72, 81, 99, 
108, 117, 126, 135, 144, 153, 162, 
171, 180, 198, 207, 216, 225, 234, 
243, 252, 261, 279, 297, 306, 315, 
324, 333, 342, 351, 360, 378, 396,
405, 414, 423, 432, 441, ...

I'm not sure, though, because you
have usually gaps of 9 units between 
two consecutive terms, and sometimes
gaps of 18 units... I don't know how
to handle algorithmically those.

Best,
É.