[seqfan] Cut the sequence after it's 1s

[Eric Angelini]

Hello SeqFans,
More self-describing sequences with a knife...

Cut the sequence C(1) after every digit "1".
The digit-size of each chunk is given by C(1) itself.
C(1) was always extended with the smallest integer no yet 
present in C(1) and not leading to a contradiction. 
Thus is C(1) the lexicographically first sequence of this
kind:

C(1)= 1,2,10,3,4,5,6,7,8,9,21,20,12,22,13,23,31,24,25,41,26,27,28,100,29,30,51,32,33,34,35,102,36,37,38,39,40,42,43,44,45,103,46,47,48,49,61,50,52,53,54,55,56,57,58,59,60,71,62,63,64,65,66,67,104,68,69,70,72,73,74,75,76,77,78,105,79,80,82,83,84,85,86,87,88,89,90,92,93,94,106,95,96,97,98,99,200,202,203,201,204,205,206,207,208,209,220,222,107,223,224,225,226,227,228,229,230,232,233,234,235,221,...

The first chunks are visible here (a star is a cut):

1,*2,1*0,3,4,5,6,7,8,9,21*,20,1*2,22,1*3,23,31*,24,25,41*,...
 1  2         10            3     4       5        6

10 sequences can be build with the same idea. None sems to
be in the OEIS. Here is how C(2) starts:

C(2)=
3,1,2,20,21,3,4,5,6,7,8,9,10,11,13,14,15,16,23,17,18,19,30,31,33,34,35,36,12,...

Digit-chunks:

3,1,2*,2*0,2*1,4,5,6,7,8,9,10,11,13,14,15,16,2*3,17,18,19,30,31,33,34,35,36,12*,...
  3    1  2               20                                  21

Here is how C(3) starts, I guess:

C(3)=
2,3,1,4,33,5,6,7,30,8,9,10,11,12,14,15,16,17,18,19,20,21,22,24,25,13,26,27,31,28,29,32,40,41,23,...

Digit-chunks:

2,3*,1,4,3*3*,5,6,7,3*0,8,9,10,11,12,14,15,16,17,18,19,20,21,22,24,25,13*,26,27,3*1,28,29,3*2,40,41,23*,...
 2     3   1     4                             33                            5         6        7

... and here is how C(0) might look:

C(0)=
3,10,1,2,4,5,6,7,8,9,100,20,11,30,12,110,13,14,40,15,16,120,...

Digit-chunks:
3,10*,1,2,4,5,6,7,8,9,10*0*,20*,11,30*,12,110*,13,14,40*,15,16,120*,...
  3          10          1  2    4       5        6          7

Best,
É.