(In reply to a proof
My guess is the list of non-champagnat numbers is finite.
Not only do they dwindle, but they dwindle fast once you add a couple digits.
Consider 5 digit numbers. Each has a max sod of 9*5=45 so a very weak upper bound is 10000/45=222.22 numbers in any string. Each string then contains at least 4 champ numbers (222/45). Again this is a very weak upper bound.
But if every starting number has to give us 4 champ numbers it would be very unlikely for a number to get missed every time.
For 6 digits the same reasoning gives 100000/54^2=34.29 champ numbers for each string. It would be awful hard for a potential champ to slip through.
Posted by Jer
on 2018-01-23 16:01:25