Terms share no digit with their difference

[Jack Brennen]

Jack Brennen wrote:
> The sequence can be infinite, correct?
> 
> 1, 3, 11, 33, 111, 333, 1111, 3333, ...
> 
> I suppose one might ask for the densest (or slowest growing)
> such infinite sequence...
> 

This example of such a sequence appears to end up in a pattern which
appears at first glance to be repeatable infinitely and grows basically
as slow as possible:


1 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9 -> 17 -> 26 -> 37 -> 49 -> 57 -> 69 
-> 77 -> 88 -> 95 -> 177 -> 266 -> 385 -> 497 -> 558 -> 699 -> 707 -> 
866 -> 979 -> 1585 -> 2292 -> 3866 -> 4977 -> 5588 -> 6992 -> 7077 -> 
8668 -> 9793 -> 15855 -> 22929 -> 38686 -> 49797 -> 55858 -> 69962 -> 
70777 -> 86688 -> 97939 -> 158585 -> 229292 -> 386866 -> 497977 -> 
558588 -> 699662 -> 707777 -> 866888 -> 979393 -> 1585855 -> 2292929 -> 
3868686 -> 4979797 -> 5585858 -> 6996632 -> 7077777


I don't think this particular sequence is necessarily worthy of
inclusion in the OEIS because I suspect there are many such
sequences, this just happens to be the one I found.