[seqfan] As much as I hate "base" sequences...

[David Wilson]

Start with k and repeatedly apply the function

k -> k / sum of digits of k

stopping when there is a positive remainder or the divisor is 1.

The smallest survivors of n iterations among the 29-smooth numbers are

0 1
1 2
2 12
3 108
4 1944
5 52488
6 1102248
7 44641044
8 1008000000
9 10080000000
10 100800000000
11 1008000000000
12 10080000000000
13 100800000000000
14 1008000000000000
15 10080000000000000
16 100800000000000000
17 1008000000000000000
18 10080000000000000000

I am all but certain that these are these are indeed the smallest survivors
among the integers, and that the sequence extends to infinity in the obvious
way.

The change in behavior at a(8) surprised me at first. a(1) through a(7)
eventually reach 1.  For n >= 8, we have

a(n) = 1008*10^(n-2) ->  112*10^(n-2) -> 28*10^(n-2) -> 28*10^(n-3) -> ...
-> 28.

ending at 28 after n iterations.