All digits d of n become d+1

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.

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[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.