a(n) is the least positive integer not yet in the sequence which shares a digit with either a(n-3) or a(n-2) (or with both), but shares no digit with a(n-1); a(1)=0, a(2)=1, a(3)=2.
Apparently there exist only 5 pairs of consecutive integers belonging this sequence, a(k+1)-a(k)=1 for k in (1,2,10,18,26). Respectively those pairs are: (0;1), (1;2), (3;4), (5;6), and (7;8).
It seems that a(j)=j only for j in (12,14,31,53,55,60,71,73,75,82,84,95,102). - R. J. Cano, Apr 22 2018
