two "find the next term" puzzles from Knuth Vol 4

[N. J. A. Sloane]

the two puzzles (and their solutions) are

%I A123896
%S A123896 0,1,1,1,12,12,12,12,12,12,100,121,122,123,123
%N A123896 A123895(n^2).
...

%I A123902
%S A123902 0,1,12,100,112,121,122,123
%N A123902 A123896 sorted and uniqued.
...

which are based on this:

%I A123895
%S A123895 0,1,1,1,1,1,1,1,1,1,10,11,12,12,12,12,12,12,12,12,10,12,11,12,12,
%T A123895 12,12,12,12,12,10,12,12,11,12,12,12,12,12,12,10,12,12,12,11,12,12,
%U A123895 12,12,12,10,12,12,12,12,11,12,12,12,12,10,12,12,12,12,12,11,12,12
%N A123895 Restricted growth string for the (decimal expansion of the) number n.
%C A123895 Write n in base 10 prefixed with a 0. Read this string from left to r
ight. Write a 0 each time you see the first distinct digit (which is 0), write a
1 each time you see the second distinct digit, write a 2 each time you see the t
hird distinct digit, and so on. Finally, delete the leading zeros.
%D A123895 D. E. Knuth, TAOCP, Vol. 4, Section 7.2.1.5, Problems 4 and 5.
%e A123895 To find a(66041171): 066041171 -> 011023343 -> 11023343.
%Y A123895 Cf. A123896, A123902.
%K A123895 nonn,base,new
%O A123895 0,11
%A A123895 njas, Nov 20 2006

It would be nice if someone could extend the first two, and provide
maple or mma or other code for the third one

Neil