[seqfan] Strings resurrection

[Eric Angelini]

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.