Yes, it's very interesting how 7 is so often the one problem non-divisor when all the others fit neatly in. I also encountered that in the course of building up to that remarkable number in my previous post. (I'm not bragging, the number's remarkable, not me). For example
works for each digit except 7 or 777. Damn! It's only when I got up to groups of six repdigits that 7 finally toed the line along with all the others and divided in where it should. Yet golly, when it does divide it does so in spades.
Look at that number again:
Each individual repdigit group of six is divisible by 7. Not only that, each successive group of groups is as well. For example 111111222222 is, and 111111222222333333, and so on.
I'm not going any further for now. After six digits I shall rest with the seventh.