[seqfan] Digitsum and length

[Éric Angelini]

Hello SeqFans,
say that "The digitsum of a(n) is the 
length of a(n+1)" -- we then get (with S
being the lexicographically earliest 
seq of such distinct integers):
S = 1,2,10,3,100,4,1000,5,10000,6,100000,
7,1000000,8,10000000,9,100000001,
11,12,101,12,1001,...
We see above after 9 that the next 
integer cannot be 100000000 (length  9)
because this integer has digitsum 1 and
all integers with digitsum 1 have been
used already in S; thus 100000001
after 9 (with digitsum 2), followed by 
11 (length 2), as 10 (same length) is 
already in S.
S is infinite, of course, but in computing 
its terms one must be careful because 
of this "limited available lengths" story.
Any takers (if interested)? -- I'd love to
see a 100000001-term graph (!)
Best,
É.