(In reply to computer solution
There is no base lower than 7 with matryoshkas with distinct digits.
7 2564 2 19 139 977 is the 1st valid entry
The long list definitely needs revision.
I suggest reducing the output to include only the minimal and maximal values (distinct digits only) for all bases below 24(a reasonable choice) or other number of your choice.
I understand 36 was chosen not to exceed the letters of the English ABC, but 16, 20 or 24 will do as well.
Edited on March 3, 2016, 7:39 pm