The answer is no, as it is impossible to find a term of k digits that comes after a term of k-1 digits. If we ask to a(n), a(n+1) and their _product_ to share at least one identical substring we have a lexico-infinite seq that starts, I guess, with: 1, 10, 11, 12, 2, 21, 15, 5, 25, ... and the successive shared substrings are: 1 1 1 2 2 1 5 5 etc. Best, É.

Hello Math-Fun ... 1199, 1200, 1220, 1222, 1224, 1248,... If we compute a(n) - a(n+1) we notice that the result is a substring of both a(n) and a(n+1). The above example gives: 1199, 1200, 1220, 1222, 1224, 1248,... 1 20 2 2 24 Question: is an infinite such seq possible?