[seqfan] Sum of a(n-1) and a(n)'s first digit

[Eric Angelini]

Hello Seqfans,
let a(n) be the sum of a(n-1) and a(n)'s first digit.

Example : a(n-1) = 597
          a(n)   = 603  (as 597 + 6 = 603)

This doesn't work sometimes:

Example : a(n-1) = 991
          a(n) = ?

Is there an infinite such sequence?

If you start the sequence with 0,9,... you might be
stuck: ..., 68, 75, 83, 92, ?

But there is a way to jump over 100: simply select this
branch:

0,9,10,11,12,13,14,15,16,17,18,20,22,...

instead of:

0,9,10,11,12,13,14,15,16,17,18,19,21,...

The first branch leads to ..., 68, 75, 83, 92.
The second one to ...  54, 60, 66, 73, 81, 90, 99, 100, 101, ...

Best,
É.