**All digits d of n
become d+1**

Hello SeqFans,

Start with n = 127.
Replace, one by one, every digit 'd' of n by 'd+1'.
Iterate.

127 -> 238 ->
349 -> 4510 -> 5621 -> 6732...

Questions:

*Will the substring
<127> reappear at some stage in the iteration of 127?

*If yes, after how
many steps?

*Can we assign to
n=1, n=2, n=3, etc., the number of steps needed to see the substring <n>
reappear in the iteration of n (as defined above)?

*If we go backwards,
we can see that 905 will produce the substring <127> in 2 steps:

905 -> 1016 ->
2127 (hit). Is 905 the smallest integer producing 127?

*What are the
smallest "ancestors" of n=1, n=2, n=3, ...
producing the substring <n>?

Best,

É.

----------

[**Maximilian Hasler**] :

http://oeis.org/A216556 Concatenate decimal digits of n,
each increased by 1

http://oeis.org/A216557 Iterations of A216556 until n reappears
as substring

http://oeis.org/A216587 Preimage
of n for A216556

http://oeis.org/A216589 Numbers n which don't have a preimage for A216556

http://oeis.org/A216603 Indices n for which A216557(n)=0

Merci Maximilian !

à+

É.