Another way to make the seq infinite is to ask that a(n) always has one of its digits that divides a(n-1). If we start with "1" we'll get: T=1,10,2,11,12,3,13,14,7,15,5,16,4,17,18,9,... As always, a(n) must be the smallest available integer not present so far in T. [this is not http://oeis.org/A248024] Best, É.