First differences palindrome

Hello Math-Fun,
Look at the finite seq S:
S = 63, 1, 42, 6.
The successive first differences of S are:
D = 62, 41, 36.
The digits of D are the digits of S read backwards.

I found also those trivial examples:
S = 0, 11, 1
S = 0, 22, 2
S = 0, 33, 3
etc.

Questions:
a) What is the lexicographically shortest S containing the digits 0 to 9 at least once?
    [I don’t know]
b) Does someone have an idea about how this could enter the OEIS?
Best,
É.
____________
Next day update

Gilles E.-F. was quick to send me this:

 5, 54,  9, 4 --> 49, 45,  5
13,  1, 32, 1 --> 12, 31, 31
26,  2, 64, 2 --> 24, 62, 62
39,  3, 96, 3 --> 36, 93, 93
63,  1, 42, 6 --> 62, 41, 36
76,  2, 74, 7 --> 74, 72, 67

 7, 20, 64, 4, 31 --> 13, 44, 60, 27

7 digits out of 10 — the hunt continues, bravo Gilles!
On my side, I've just found this:

 4, 60, 71, 1, 65 --> 56, 11, 70, 64

____________
June 18th update

A legitimate question is this one: could such a first differences palindrome be infinite? The answer is yes – and here is how Gilles E.-F. and the author found an example.

The first step was to construct the "bricks" A and B:
A = 23, 32, 9
B = 41, 32, 9
We now assemble an infinite amount of bricks A, then stop at some point (the "center") and assemble from there an infinite amount of bricks B. We get:

S = ......AAAAAAABBBBBBB......

S = ......23, 32, 9, 23, 32, 9, 23, 32, 9, 41, 32, 9, 41, 32, 9, 41, 32, 9,......

The successive first differences D of the above S introduce the new brick C (in pink/red):


Gilles found a way to "sew" the two exterior borders of S. This allows to build sequences S of any (finite) size (provided the number of terms of S is a multiple of 6).

Left border seam: 1, 13, 32, 9
Right border seam: 12, 1

The above "three yellow bricks" S becomes, for instance:

We have indeed here a finite sequence S on top of its first differences D – and the digits of D are the digits of S read backwards. 

Bravo and thousand one thanks, Gilles!
_____________________
June 20th 2023 update

Gilles has computed many interesting things – and found a lot of answers to the above pandigital question. Hereunder are a few short results he found (short means that S has only three terms (less than three terms for S is impossible). As usual, D are the first absolute differences of S, which, read backwards, rebuild S):

 S = 363726,175571802934,175571 --> D = 175571439208,175571627363
 S = 363726,193391820754,193391 --> D = 193391457028,193391627363
 S = 363726,274472901835,274472 --> D = 274472538109,274472627363
 S = 363726,283382910745,283382 --> D = 283382547019,283382627363
 S = 726363,382283745910,382283 --> D = 382283019547,382283363627
 S = 726363,391193754820,391193 --> D = 391193028457,391193363627
 S = 726363,472274835901,472274 --> D = 472274109538,472274363627
 S = 726363,490094853721,490094 --> D = 490094127358,490094363627
 S = 726363,571175934802,571175 --> D = 571175208439,571175363627
 S = 726363,580085943712,580085 --> D = 580085217349,580085363627

[For a 297-solution list, please go to the very end of this page]

What about other bases? Gilles also found many interesting pandigital solutions for the bases 2 to 18:

Base 2 pandigital (3 terms): S = 0,11,1 --> D = 11,10

Base 3 pandigital (3 terms): S = 11,220,2 --> D = 202,211
Base 3 pandigital (4 terms): S = 1,0,222,21 --> D = 1,222,201
Base 3 pandigital (4 terms): S = 10,221,1,2 --> D = 211,220,
Base 3 pandigital (5 terms): S = 1,0,22,2,1 --> D = 1,22,20,1

Base 4 pandigital (4 terms): S = 3,0,122,13 --> D = 3,122,103
Base 4 pandigital (4 terms): S = 10,332,2,3 --> D = 322,330,1
Base 4 pandigital (6 terms): S = 2,3,0,3,33,1 --> D = 1,3,3,30,32

Base 5 pandigital (3 terms): S = 31,2240,22 --> D = 2204,2213
Base 5 pandigital (6 terms): S = 4,22,2,0,2,31 --> D = 13,20,2,2,24

Base 6 pandigital (3 terms): S = 2134,10015313,1001 --> D = 10013135,10014312
Base 6 pandigital (5 terms): S = 2,40,51,1,43 --> D = 34,11,50,42

Base 7 pandigital (3 terms): S = 2244,13316053,1331 --> D = 13313506,13314422
Base 7, 3 terms, 6 digits (no duplicates): S = 61,523,4 --> D = 432,516
Base 7, 5 terms, 6 distinct digits: S = 2,61,24,3,65 --> D = 56,34,21,62
Base 7, 5 terms, 6 distinct digits: S = 4,20,64,4,31 --> D = 13,44,60,24

Base 8 pandigital (3 terms): S = 3245,16617304,1661 --> D = 16614037,16615423
Base 8, 5 terms, 7 distinct digits: S = 5,20,64,4,31 --> D = 13,44,60,25

Base 9 pandigital (3 terms): S = 32856,1000175824,10001 --> D = 1000142857,1000165823

Base 11 pandigital (3 terms): S = 43A67,1828194205,18281 --> D = 1828150249,1828176A34

Base 12 pandigital (3 terms): S = 83B74,521259A061,52125 --> D = 52125160A9,5212547B38

Base 13 pandigital (3 terms): S = 4840938,1B707B1A230C65,1B707B1 --> D = 1B707B156C032A,1B707B18390484

Base 14 pandigital (3 terms): S = 504D8D9,13CAC31B37A236,13CAC31 --> D = 13CAC31632A73B,13CAC319D8D405

Base 15 pandigital (3 terms): S = 5A4E94A,17D0D71BC80326,17D0D71 --> D = 17D0D7162308CB,17D0D71A49E4A5

Base 16 pandigital (3 terms): S = 5A5000B4A,1D89F98D1C239F9E76,1D89F98D1 --> D = 1D89F98D167E9F932C,1D89F98D1A4B0005A5

Base 17 pandigital (3 terms): S = 5A5000B4A,1D89F98D1C239F9E76,1D89F98D1 --> D = 1D89F98D167E9F932C,1D89F98D1A4B0005A5

Base 18 pandigital (3 terms): S = 6665HBBBC, 12FG0GF21DE9A04387, 12FG0GF21 --> 12FG0GF2178340A9ED, 12FG0GF21CBBBH5666

That's all Folks !
Many thanks to Gilles, again!

[The above promised 297-solution list is hereunder]

9 distinct digits and 3 terms:
S = 33066,1656182594,16561 --> D = 1656149528,1656166033
9 distinct digits and 3 terms:
S = 33066,1676182794,16761 --> D = 1676149728,1676166033
9 distinct digits and 3 terms:
S = 33066,2414290175,24142 --> D = 2414257109,2414266033
9 distinct digits and 3 terms:
S = 33066,2484290875,24842 --> D = 2484257809,2484266033
9 distinct digits and 3 terms:
S = 33066,2545291485,25452 --> D = 2545258419,2545266033
9 distinct digits and 3 terms:
S = 33066,2575291785,25752 --> D = 2575258719,2575266033
9 distinct digits and 3 terms:
S = 66033,4212475190,42124 --> D = 4212409157,4212433066
9 distinct digits and 3 terms:
S = 66033,4282475890,42824 --> D = 4282409857,4282433066
9 distinct digits and 3 terms:
S = 66033,5242585491,52425 --> D = 5242519458,5242533066
9 distinct digits and 3 terms:
S = 66033,5272585791,52725 --> D = 5272519758,5272533066
9 distinct digits and 3 terms:
S = 66033,6151694582,61516 --> D = 6151628549,6151633066
9 distinct digits and 3 terms:
S = 66033,6171694782,61716 --> D = 6171628749,6171633066
 
8 distinct digits and 3 terms:
S = 3366,24429075,2442 --> D = 24425709,24426633
8 distinct digits and 3 terms:
S = 6633,42247590,4224 --> D = 42240957,42243366
 
7 distinct digits and 3 terms:
S = 396,111804,111 --> D = 111408,111693
7 distinct digits and 3 terms:
S = 396,121814,121 --> D = 121418,121693
7 distinct digits and 3 terms:
S = 396,131824,131 --> D = 131428,131693
7 distinct digits and 3 terms:
S = 396,151844,151 --> D = 151448,151693
7 distinct digits and 3 terms:
S = 396,161854,161 --> D = 161458,161693
7 distinct digits and 3 terms:
S = 396,171864,171 --> D = 171468,171693
7 distinct digits and 3 terms:
S = 396,181874,181 --> D = 181478,181693
7 distinct digits and 3 terms:
S = 396,212905,212 --> D = 212509,212693
7 distinct digits and 3 terms:
S = 396,282975,282 --> D = 282579,282693
7 distinct digits and 5 terms:
S = 7,20,64,4,31 --> D = 13,44,60,27
 
6 distinct digits (no duplicates) and 3 terms:
S = 91,523,4 --> D = 432,519
6 distinct digits and 5 terms:
S = 4,60,71,1,65 --> D = 56,11,70,64
6 distinct digits and 5 terms:
S = 5,94,57,3,98 --> D = 89,37,54,95
6 distinct digits and 5 terms:
S = 6,30,96,6,42 --> D = 24,66,90,36
6 distinct digits and 5 terms:
S = 72,42,6,30,3 --> D = 30,36,24,27
6 distinct digits and 6 terms:
S = 4,19,3,6,15,1 --> D = 15,16,3,9,14
 
5 distinct digits and 3 terms:
S = 45,761,7 --> D = 716,754
5 distinct digits and 3 terms:
S = 64,348,2 --> D = 284,346
5 distinct digits and 3 terms:
S = 82,835,7 --> D = 753,828
5 distinct digits and 4 terms:
S = 63,1,42,6 --> D = 62,41,36
5 distinct digits and 5 terms:
S = 2,46,18,2,44 --> D = 44,28,16,42
5 distinct digits and 5 terms:
S = 2,80,25,5,87 --> D = 78,55,20,82
5 distinct digits and 6 terms:
S = 2,5,0,11,1,53 --> D = 3,5,11,10,52
5 distinct digits and 6 terms:
S = 2,7,0,33,3,75 --> D = 5,7,33,30,72
5 distinct digits and 6 terms:
S = 2,8,0,44,4,86 --> D = 6,8,44,40,82
5 distinct digits and 6 terms:
S = 2,9,0,55,5,97 --> D = 7,9,55,50,92
5 distinct digits and 6 terms:
S = 4,9,0,11,1,95 --> D = 5,9,11,10,94
5 distinct digits and 6 terms:
S = 4,30,63,3,6,2 --> D = 26,33,60,3,4
5 distinct digits and 6 terms:
S = 6,13,1,32,1,7 --> D = 7,12,31,31,6
5 distinct digits and 6 terms:
S = 9,22,2,0,2,31 --> D = 13,20,2,2,29
5 distinct digits and 6 terms:
S = 9,33,3,0,3,42 --> D = 24,30,3,3,39
5 distinct digits and 12 terms:
S = 1,13,32,9,23,32,9,41,32,9,12,1 --> D = 12,19,23,14,9,23,32,9,23,3,11
5 distinct digits and 18 terms : 1,13,32,9,23,32,9,23,32,9,41,32,9,41,32,9,12,1 --> D = 12,19,23,14,9,23,14,9,23,32,9,23,32,9,23,3,11
5 distinct digits and 24 terms:
S = 1,13,32,9,23,32,9,23,32,9,23,32,9,41,32,9,41,32,9,41,32,9,12,1 --> D = 12,19,23,14,9,23,14,9,23,14,9,23,32,9,23,32,9,23,32,9,23,3,11
5 distinct digits and 30 terms:
S = 1,13,32,9,23,32,9,23,32,9,23,32,9,23,32,9,41,32,9,41,32,9,41,32,9,41,32,9,12,1 --> D = 12,19,23,14,9,23,14,9,23,14,9,23,14,9,23,32,9,23,32,9,23,32,9,23,32,9,23,3,11
5 distinct digits and 36 terms:
S = 1,13,32,9,23,32,9,23,32,9,23,32,9,23,32,9,23,32,9,41,32,9,41,32,9,41,32,9,41,32,9,41,32,9,12,1 --> D = 12,19,23,14,9,23,14,9,23,14,9,23,14,9,23,14,9,23,32,9,23,32,9,23,32,9,23,32,9,23,32,9,23,3,11

Remark:
5 distinct digits and 6n terms, n >= 2 : 1,13,32,9,[23,32,9],[41,32,9],12,1. This works for n = 1 too, but leads to 4 distinct digits only.
 
4 distinct digits and 3 terms:
S = 18,586,5 --> D = 568,581
4 distinct digits and 4 terms:
S = 10,332,2,3 --> D = 322,330,1
4 distinct digits and 4 terms:
S = 10,443,3,4 --> D = 433,440,1
4 distinct digits and 4 terms:
S = 10,554,4,5 --> D = 544,550,1
4 distinct digits and 4 terms:
S = 10,665,5,6 --> D = 655,660,1
4 distinct digits and 4 terms:
S = 10,776,6,7 --> D = 766,770,1
4 distinct digits and 4 terms:
S = 10,887,7,8 --> D = 877,880,1
4 distinct digits and 4 terms:
S = 10,998,8,9 --> D = 988,990,1
4 distinct digits and 4 terms:
S = 20,331,1,3 --> D = 311,330,2
4 distinct digits and 4 terms:
S = 20,553,3,5 --> D = 533,550,2
4 distinct digits and 4 terms:
S = 20,664,4,6 --> D = 644,660,2
4 distinct digits and 4 terms:
S = 20,775,5,7 --> D = 755,770,2
4 distinct digits and 4 terms:
S = 20,886,6,8 --> D = 866,880,2
4 distinct digits and 4 terms:
S = 20,997,7,9 --> D = 977,990,2
4 distinct digits and 4 terms:
S = 30,441,1,4 --> D = 411,440,3
4 distinct digits  and 4 terms:
S = 30,552,2,5 --> D = 522,550,3
4 distinct digits and 4 terms:
S = 30,774,4,7 --> D = 744,770,3
4 distinct digits and 4 terms:
S = 30,885,5,8 --> D = 855,880,3
4 distinct digits and 4 terms:
S = 30,996,6,9 --> D = 966,990,3
4 distinct digits and 4 terms:
S = 40,551,1,5 --> D = 511,550,4
4 distinct digits and 4 terms:
S = 40,662,2,6 --> D = 622,660,4
4 distinct digits and 4 terms:
S = 40,773,3,7 --> D = 733,770,4
4 distinct digits and 4 terms:
S = 40,995,5,9 --> D = 955,990,4
4 distinct digits and 4 terms:
S = 50,661,1,6 --> D = 611,660,5
4 distinct digits and 4 terms:
S = 50,772,2,7 --> D = 722,770,5
4 distinct digits and 4 terms:
S = 50,883,3,8 --> D = 833,880,5
4 distinct digits and 4 terms:
S = 50,994,4,9 --> D = 944,990,5
4 distinct digits and 4 terms:
S = 60,771,1,7 --> D = 711,770,6
4 distinct digits and 4 terms:
S = 60,882,2,8 --> D = 822,880,6
4 distinct digits and 4 terms:
S = 60,993,3,9 --> D = 933,990,6
4 distinct digits and 4 terms:
S = 70,881,1,8 --> D = 811,880,7
4 distinct digits and 4 terms:
S = 70,992,2,9 --> D = 922,990,7
4 distinct digits and 4 terms:
S = 76,2,74,7 --> D = 74,72,67
4 distinct digits and 4 terms:
S = 80,991,1,9 --> D = 911,990,8
4 distinct digits and 6 terms:
S = 1,13,32,9,12,1 --> D = 12,19,23,3,11
4 distinct digits and 6 terms:
S = 2,3,0,3,33,1 --> D = 1,3,3,30,32
4 distinct digits and 6 terms:
S = 2,3,33,0,3,1 --> D = 1,30,33,3,2
4 distinct digits and 6 terms:
S = 2,5,0,5,55,3 --> D = 3,5,5,50,52
4 distinct digits and 6 terms:
S = 2,5,55,0,5,3 --> D = 3,50,55,5,2
4 distinct digits and 6 terms:
S = 2,6,0,6,66,4 --> D = 4,6,6,60,62
4 distinct digits and 6 terms:
S = 2,6,0,22,2,64 --> D = 4,6,22,20,62
4 distinct digits and 6 terms:
S = 2,6,66,0,6,4 --> D = 4,60,66,6,2
4 distinct digits and 6 terms:
S = 2,7,0,7,77,5 --> D = 5,7,7,70,72
4 distinct digits and 6 terms:
S = 2,7,77,0,7,5 --> D = 5,70,77,7,2
4 distinct digits and 6 terms:
S = 2,8,0,8,88,6 --> D = 6,8,8,80,82
4 distinct digits and 6 terms:
S = 2,8,88,0,8,6 --> D = 6,80,88,8,2
4 distinct digits and 6 terms:
S = 2,9,0,9,99,7 --> D = 7,9,9,90,92
4 distinct digits and 6 terms:
S = 2,9,99,0,9,7 --> D = 7,90,99,9,2
4 distinct digits and 6 terms:
S = 4,5,0,5,55,1 --> D = 1,5,5,50,54
4 distinct digits and 6 terms:
S = 4,5,55,0,5,1 --> D = 1,50,55,5,4
4 distinct digits and 6 terms:
S = 4,6,0,6,66,2 --> D = 2,6,6,60,64
4 distinct digits and 6 terms:
S = 4,6,66,0,6,2 --> D = 2,60,66,6,4
4 distinct digits and 6 terms:
S = 4,7,0,7,77,3 --> D = 3,7,7,70,74
4 distinct digits and 6 terms:
S = 4,7,77,0,7,3 --> D = 3,70,77,7,4
4 distinct digits and 6 terms:
S = 4,9,0,9,99,5 --> D = 5,9,9,90,94
4 distinct digits and 6 terms:
S = 4,9,99,0,9,5 --> D = 5,90,99,9,4
4 distinct digits and 6 terms:
S = 6,7,0,7,77,1 --> D = 1,7,7,70,76
4 distinct digits and 6 terms:
S = 6,7,77,0,7,1 --> D = 1,70,77,7,6
4 distinct digits and 6 terms:
S = 6,8,0,8,88,2 --> D = 2,8,8,80,86
4 distinct digits and 6 terms:
S = 6,8,88,0,8,2 --> D = 2,80,88,8,6
4 distinct digits and 6 terms:
S = 6,9,0,9,99,3 --> D = 3,9,9,90,96
4 distinct digits and 6 terms:
S = 6,9,99,0,9,3 --> D = 3,90,99,9,6
4 distinct digits and 6 terms:
S = 7,8,0,8,88,1 --> D = 1,8,8,80,87
4 distinct digits and 6 terms:
S = 7,8,88,0,8,1 --> D = 1,80,88,8,7
4 distinct digits and 6 terms:
S = 7,9,0,9,99,2 --> D = 2,9,9,90,97
4 distinct digits and 6 terms:
S = 7,9,99,0,9,2 --> D = 2,90,99,9,7
4 distinct digits and 6 terms:
S = 8,9,0,9,99,1 --> D = 1,9,9,90,98
4 distinct digits and 6 terms:
S = 8,9,99,0,9,1 --> D = 1,90,99,9,8
 
3 distinct digits and 3 terms:
S = 27,274,2 --> D = 247,272
3 distinct digits and 4 terms:
S = 5,54,9,4 --> D = 49,45,5
3 distinct digits and 4 terms:
S = 10,221,1,2 --> D = 211,220,1
3 distinct digits and 4 terms:
S = 13,1,32,1 --> D = 12,31,31
3 distinct digits and 4 terms:
S = 20,442,2,4 --> D = 422,440,2
3 distinct digits and 4 terms:
S = 26,2,64,2 --> D = 24,62,62
3 distinct digits and 4 terms:
S = 30,663,3,6 --> D = 633,660,3
3 distinct digits and 4 terms:
S = 39,3,96,3 --> D = 36,93,93
3 distinct digits and 4 terms:
S = 40,884,4,8 --> D = 844,880,4
3 distinct digits and 5 terms:
S = 1,0,22,2,1 --> D = 1,22,20,1
3 distinct digits and 5 terms:
S = 1,2,22,0,21 --> D = 1,20,22,21
3 distinct digits and 5 terms:
S = 2,0,44,4,2 --> D = 2,44,40,2
3 distinct digits and 5 terms:
S = 2,4,44,0,42 --> D = 2,40,44,42
3 distinct digits and 5 terms:
S = 3,0,66,6,3 --> D = 3,66,60,3
3 distinct digits and 5 terms:
S = 3,6,66,0,63 --> D = 3,60,66,63
3 distinct digits and 5 terms:
S = 4,0,88,8,4 --> D = 4,88,80,4
3 distinct digits and 5 terms:
S = 4,8,88,0,84 --> D = 4,80,88,84
3 distinct digits and 5 terms:
S = 12,0,2,22,1 --> D = 12,2,20,21
3 distinct digits and 5 terms:
S = 24,0,4,44,2 --> D = 24,4,40,42
3 distinct digits and 5 terms:
S = 36,0,6,66,3 --> D = 36,6,60,63
3 distinct digits and 5 terms:
S = 48,0,8,88,4 --> D = 48,8,80,84
3 distinct digits and 6 terms:
S = 2,4,0,4,44,2 --> D = 2,4,4,40,42
3 distinct digits and 6 terms:
S = 2,4,44,0,4,2 --> D = 2,40,44,4,2
3 distinct digits and 6 terms:
S = 4,8,0,8,88,4 --> D = 4,8,8,80,84
3 distinct digits and 6 terms:
S = 4,8,88,0,8,4 --> D = 4,80,88,8,4
 
2 distinct digits and 3 terms:
S = 0,11,1 --> D = 11,10
2 distinct digits nd 3 terms:
S = 0,22,2 --> D = 22,20
2 distinct digits and 3 terms:
S = 0,33,3 --> D = 33,30
2 distinct digits and 3 terms:
S = 0,44,4 --> D = 44,40
2 distinct digits and 3 terms:
S = 0,55,5 --> D = 55,50
2 distinct digits and 3 terms:
S = 0,66,6 --> D = 66,60
2 distinct digits and 3 terms:
S = 0,77,7 --> D = 77,70
2 distinct digits and 3 terms:
S = 0,88,8 --> D = 88,80
2 distinct digits and 3 terms:
S = 0,99,9 --> D = 99,90
2 distinct digits and 4 terms:
S = 1,11,0,1 --> D = 10,11,1
2 distinct digits and 4 terms:
S = 2,22,0,2 --> D = 20,22,2
2 distinct digits and 4 terms:
S = 3,33,0,3 --> D = 30,33,3
2 distinct digits and 4 terms:
S = 4,44,0,4 --> D = 40,44,4
2 distinct digits and 4 terms:
S = 5,55,0,5 --> D = 50,55,5
2 distinct digits and 4 terms:
S = 6,66,0,6 --> D = 60,66,6
2 distinct digits and 4 terms:
S = 7,77,0,7 --> D = 70,77,7
2 distinct digits and 4 terms:
S = 8,88,0,8 --> D = 80,88,8
2 distinct digits and 4 terms:
S = 9,99,0,9 --> D = 90,99,9
2 distinct digits and 4 terms:
S = 10,110,0,1 --> D = 100,110,1
2 distinct digits and 4 terms:
S = 20,220,0,2 --> D = 200,220,2
2 distinct digits and 4 terms:
S = 30,330,0,3 --> D = 300,330,3
2 distinct digits and 4 terms:
S = 40,440,0,4 --> D = 400,440,4
2 distinct digits and 4 terms:
S = 50,550,0,5 --> D = 500,550,5
2 distinct digits and 4 terms:
S = 60,660,0,6 --> D = 600,660,6
2 distinct digits and 4 terms:
S = 70,770,0,7 --> D = 700,770,7
2 distinct digits and 4 terms:
S = 80,880,0,8 --> D = 800,880,8
2 distinct digits and 4 terms:
S = 90,990,0,9 --> D = 900,990,9
2 distinct digits and 4 terms:
S = 100,1100,0,1 --> D = 1000,1100,1
2 distinct digits and 4 terms:
S = 200,2200,0,2 --> D = 2000,2200,2
2 distinct digits and 4 terms:
S = 300,3300,0,3 --> D = 3000,3300,3
2 distinct digits and 4 terms:
S = 400,4400,0,4 --> D = 4000,4400,4
2 distinct digits and 4 terms:
S = 500,5500,0,5 --> D = 5000,5500,5
2 distinct digits and 4 terms:
S = 600,6600,0,6 --> D = 6000,6600,6
2 distinct digits and 4 terms:
S = 700,7700,0,7 --> D = 7000,7700,7
2 distinct digits and 4 terms:
S = 800,8800,0,8 --> D = 8000,8800,8
2 distinct digits and 4 terms:
S = 900,9900,0,9 --> D = 9000,9900,9
2 distinct digits and 4 terms:
S = 1000,11000,0,1 --> D = 10000,11000,1
2 distinct digits and 4 terms:
S = 2000,22000,0,2 --> D = 20000,22000,2
2 distinct digits and 4 terms:
S = 3000,33000,0,3 --> D = 30000,33000,3
2 distinct digits nd 4 terms:
S = 4000,44000,0,4 --> D = 40000,44000,4
2 distinct digits and 4 terms:
S = 5000,55000,0,5 --> D = 50000,55000,5
2 distinct digits and 4 terms:
S = 6000,66000,0,6 --> D = 60000,66000,6
2 distinct digits and 4 terms:
S = 7000,77000,0,7 --> D = 70000,77000,7
2 distinct digits and 4 terms:
S = 8000,88000,0,8 --> D = 80000,88000,8
2 distinct digits and 4 terms:
S = 9000,99000,0,9 --> D = 90000,99000,9
 
A general formula:
2 distinct digits in S and 4 terms:
S = [d*10^n, d*11*10^n, 0, d] --> D = [d*10^(n+1), d*11*10^n, d] where d is any digit except 0 and n is an integer >= 0.
This formula shows that there is no upper limit for the size of a term in S.

2 distinct digits and 6 terms:
S = 0,1,0,1,11,1 --> D = 1,1,1,10,10
2 distinct digits and 6 terms:
S = 0,1,0,11,1,11 --> D = 1,1,11,10,10
2 distinct digits and 6 terms:
S = 0,1,11,0,1,1 --> D = 1,10,11,1,0
2 distinct digits and 6 terms:
S = 0,2,0,2,22,2 --> D = 2,2,2,20,20
2 distinct digits and 6 terms:
S = 0,2,0,22,2,22 --> D = 2,2,22,20,20
2 distinct digits and 6 terms:
S = 0,2,22,0,2,2 --> D = 2,20,22,2,0
2 distinct digits and 6 terms:
S = 0,3,0,3,33,3 --> D = 3,3,3,30,30
2 distinct digits and 6 terms:
S = 0,3,0,33,3,33 --> D = 3,3,33,30,30
2 distinct digits and 6 terms:
S = 0,3,33,0,3,3 --> D = 3,30,33,3,0
2 distinct digits and 6 terms:
S = 0,4,0,4,44,4 --> D = 4,4,4,40,40
2 distinct digits and 6 terms:
S = 0,4,0,44,4,44 --> D = 4,4,44,40,40
2 distinct digits and 6 terms:
S = 0,4,44,0,4,4 --> D = 4,40,44,4,0
2 distinct digits and 6 terms:
S = 0,5,0,5,55,5 --> D = 5,5,5,50,50
2 distinct digits and 6 terms:
S = 0,5,0,55,5,55 --> D = 5,5,55,50,50
2 distinct digits and 6 terms:
S = 0,5,55,0,5,5 --> D = 5,50,55,5,0
2 distinct digits and 6 terms:
S = 0,6,0,6,66,6 --> D = 6,6,6,60,60
2 distinct digits and 6 terms:
S = 0,6,0,66,6,66 --> D = 6,6,66,60,60
2 distinct digits and 6 terms:
S = 0,6,66,0,6,6 --> D = 6,60,66,6,0
2 distinct digits and 6 terms:
S = 0,7,0,7,77,7 --> D = 7,7,7,70,70
2 distinct digits and 6 terms:
S = 0,7,0,77,7,77 --> D = 7,7,77,70,70
2 distinct digits and 6 terms:
S = 0,7,77,0,7,7 --> D = 7,70,77,7,0
2 distinct digits and 6 terms:
S = 0,8,0,8,88,8 --> D = 8,8,8,80,80
2 distinct digits and 6 terms:
S = 0,8,0,88,8,88 --> D = 8,8,88,80,80
2 distinct digits and 6 terms:
S = 0,8,88,0,8,8 --> D = 8,80,88,8,0
2 distinct digits and 6 terms:
S = 0,9,0,9,99,9 --> D = 9,9,9,90,90
2 distinct digits and 6 terms:
S = 0,9,0,99,9,99 --> D = 9,9,99,90,90
2 distinct digits and 6 terms:
S = 0,9,99,0,9,9 --> D = 9,90,99,9,0
2 distinct digits and 6 terms:
S = 0,11,1,0,1,11 --> D = 11,10,1,1,10
2 distinct digits and 6 terms:
S = 0,22,2,0,2,22 --> D = 22,20,2,2,20
2 distinct digits and 6 terms:
S = 0,33,3,0,3,33 --> D = 33,30,3,3,30
2 distinct digits and 6 terms:
S = 0,44,4,0,4,44 --> D = 44,40,4,4,40
2 distinct digits and 6 terms:
S = 0,55,5,0,5,55 --> D = 55,50,5,5,50
2 distinct digits and 6 terms:
S = 0,66,6,0,6,66 --> D = 66,60,6,6,60
2 distinct digits and 6 terms:
S = 0,77,7,0,7,77 --> D = 77,70,7,7,70
2 distinct digits and 6 terms:
S = 0,88,8,0,8,88 --> D = 88,80,8,8,80
2 distinct digits and 6 terms:
S = 0,99,9,0,9,99 --> D = 99,90,9,9,90
2 distinct digits and 6 terms:
S = 1,1,0,1,11,0 --> D = 0,1,1,10,11
2 distinct digits and 6 terms:
S = 1,1,11,0,1,0 --> D = 0,10,11,1,1
2 distinct digits and 6 terms:
S = 2,2,0,2,22,0 --> D = 0,2,2,20,22
2 distinct digits and 6 terms:
S = 2,2,22,0,2,0 --> D = 0,20,22,2,2
2 distinct digits and 6 terms:
S = 3,3,0,3,33,0 --> D = 0,3,3,30,33
2 distinct digits and 6 terms:
S = 3,3,33,0,3,0 --> D = 0,30,33,3,3
2 distinct digits and 6 terms:
S = 4,4,0,4,44,0 --> D = 0,4,4,40,44
2 distinct digits and 6 terms:
S = 4,4,44,0,4,0 --> D = 0,40,44,4,4
2 distinct digits and 6 terms:
S = 5,5,0,5,55,0 --> D = 0,5,5,50,55
2 distinct digits and 6 terms:
S = 5,5,55,0,5,0 --> D = 0,50,55,5,5
2 distinct digits and 6 terms:
S = 6,6,0,6,66,0 --> D = 0,6,6,60,66
2 distinct digits and 6 terms:
S = 6,6,66,0,6,0 --> D = 0,60,66,6,6
2 distinct digits and 6 terms:
S = 7,7,0,7,77,0 --> D = 0,7,7,70,77
2 distinct digits and 6 terms:
S = 7,7,77,0,7,0 --> D = 0,70,77,7,7
2 distinct digits and 6 terms:
S = 8,8,0,8,88,0 --> D = 0,8,8,80,88
2 distinct digits and 6 terms:
S = 8,8,88,0,8,0 --> D = 0,80,88,8,8
2 distinct digits and 6 terms:
S = 9,9,0,9,99,0 --> D = 0,9,9,90,99
2 distinct digits and 6 terms:
S = 9,9,99,0,9,0 --> D = 0,90,99,9,9
2 distinct digits and 7 terms:
S = 1,11,0,11,11,0,1 --> D = 10,11,11,0,11,1
2 distinct digits and 7 terms:
S = 1,11,1,0,1,0,1 --> D = 10,10,1,1,1,1
2 distinct digits and 7 terms:
S = 11,1,0,1,11,0,1 --> D = 10,1,1,10,11,1
2 distinct digits and 7 terms:
S = 11,1,11,0,1,0,1 --> D = 10,10,11,1,1,1
2 distinct digits and 9 terms:
S = 0,1,0,1,0,1,1,11,1 --> D = 1,1,1,1,1,0,10,10
2 distinct digits and 9 terms:
S = 0,1,0,1,0,1,11,1,11 --> D = 1,1,1,1,1,10,10,10
2 distinct digits and 9 terms:
S = 0,1,0,1,11,0,1,1,11 --> D = 1,1,1,10,11,1,0,10
2 distinct digits and 9 terms:
S = 0,1,0,11,1,0,11,11,1 --> D = 1,1,11,10,1,11,0,10
2 distinct digits and 9 terms:
S = 0,1,0,11,11,0,1,11,1 --> D = 1,1,11,0,11,1,10,10
2 distinct digits and 9 terms:
S = 0,1,11,0,11,11,0,1,1 --> D = 1,10,11,11,0,11,1,0
2 distinct digits and 9 terms:
S = 0,1,11,1,0,1,0,1,1 --> D = 1,10,10,1,1,1,1,0
2 distinct digits and 9 terms:
S = 0,11,1,0,1,1,0,1,11 --> D = 11,10,1,1,0,1,1,10
2 distinct digits and 9 terms:
S = 1,1,0,1,0,1,1,11,0 --> D = 0,1,1,1,1,0,10,11
2 distinct digits and 9 terms:
S = 1,1,0,11,1,0,11,11,0 --> D = 0,1,11,10,1,11,0,11
2 distinct digits and 9 terms:
S = 1,1,0,11,11,0,1,11,0 --> D = 0,1,11,0,11,1,10,11
2 distinct digits and 9 terms:
S = 1,1,11,0,11,11,0,1,0 --> D = 0,10,11,11,0,11,1,1
2 distinct digits and 9 terms:
S = 1,1,11,1,0,1,0,1,0 --> D = 0,10,10,1,1,1,1,1
2 distinct digits and 10 terms:
S = 1,11,0,11,11,0,11,11,0,1 --> D = 10,11,11,0,11,11,0,11,1
2 distinct digits and 10 terms:
S = 1,11,1,0,1,1,0,1,0,1 --> D = 10,10,1,1,0,1,1,1,1
2 distinct digits and 10 terms:
S = 11,1,0,1,0,1,1,11,0,1 --> D = 10,1,1,1,1,0,10,11,1
2 distinct digits and 10 terms:
S = 11,1,0,11,1,0,11,11,0,1 --> D = 10,1,11,10,1,11,0,11,1
2 distinct digits and 10 terms:
S = 11,1,0,11,11,0,1,11,0,1 --> D = 10,1,11,0,11,1,10,11,1
2 distinct digits and 10 terms:
S = 11,1,11,0,11,11,0,1,0,1 --> D = 10,10,11,11,0,11,1,1,1
2 distinct digits and 10 terms:
S = 11,1,11,1,0,1,0,1,0,1 --> D = 10,10,10,1,1,1,1,1,1
2 distinct digits and 12 terms:
S = 0,1,0,1,0,1,0,1,1,11,1,11 --> D = 1,1,1,1,1,1,1,0,10,10,10
2 distinct digits and 12 terms:
S = 0,1,0,1,0,1,0,11,11,1,11,1 --> D = 1,1,1,1,1,1,11,0,10,10,10
2 distinct digits and 12 terms:
S = 0,1,0,1,0,1,1,0,1,1,11,1 --> D = 1,1,1,1,1,0,1,1,0,10,10
2 distinct digits and 12 terms:
S = 0,1,0,1,0,10,10,0,1,1,11,1 --> D = 1,1,1,1,10,0,10,1,0,10,10
2 distinct digits and 12 terms:
S = 0,1,0,1,0,11,1,0,11,11,1,11 --> D = 1,1,1,1,11,10,1,11,0,10,10
2 distinct digits and 12 terms:
S = 0,1,0,1,0,11,11,0,1,11,1,11 --> D = 1,1,1,1,11,0,11,1,10,10,10
2 distinct digits and 12 terms:
S = 0,1,0,1,11,0,11,11,0,1,1,11 --> D = 1,1,1,10,11,11,0,11,1,0,10
2 distinct digits and 12 terms:
S = 0,1,0,1,11,1,0,1,0,1,1,11 --> D = 1,1,1,10,10,1,1,1,1,0,10
2 distinct digits and 12 terms:
S = 0,1,0,11,1,0,1,1,0,11,11,1 --> D = 1,1,11,10,1,1,0,1,11,0,10
2 distinct digits and 12 terms:
S = 0,1,0,11,11,0,11,11,0,1,11,1 --> D = 1,1,11,0,11,11,0,11,1,10,10
2 distinct digits and 12 terms:
S = 0,1,0,11,11,1,0,1,0,1,11,1 --> D = 1,1,11,0,10,1,1,1,1,10,10
2 distinct digits and 12 terms:
S = 0,1,11,0,11,11,0,11,11,0,1,1 --> D = 1,10,11,11,0,11,11,0,11,1,0
2 distinct digits and 12 terms:
S = 0,1,11,1,0,1,1,0,1,0,1,1 --> D = 1,10,10,1,1,0,1,1,1,1,0
2 distinct digits and 12 terms:
S = 0,11,1,0,1,0,11,1,11,10,11,1 --> D = 11,10,1,1,1,11,10,10,1,1,10
2 distinct digits and 12 terms:
S = 0,11,1,0,1,0,11,11,1,0,1,11 --> D = 11,10,1,1,1,11,0,10,1,1,10
2 distinct digits and 12 terms:
S = 0,11,1,0,1,1,0,1,1,0,1,11 --> D = 11,10,1,1,0,1,1,0,1,1,10
2 distinct digits and 12 terms:
S = 0,11,1,0,10,10,0,1,1,0,1,11 --> D = 11,10,1,10,0,10,1,0,1,1,10
2 distinct digits and 12 terms:
S = 0,11,1,0,11,1,0,1,11,10,11,1 --> D = 11,10,1,11,10,1,1,10,1,1,10
2 distinct digits and 12 terms:
S = 0,11,1,11,10,11,1,0,1,0,11,1 --> D = 11,10,10,1,1,10,1,1,1,11,10
2 distinct digits and 12 terms:
S = 0,11,11,1,0,1,11,0,1,0,1,1 --> D = 11,0,10,1,1,10,11,1,1,1,0
2 distinct digits and 12 terms:
S = 0,11,11,1,11,0,1,0,1,0,1,1 --> D = 11,0,10,10,11,1,1,1,1,1,0
2 distinct digits and 12 terms:
S = 1,1,0,1,0,1,0,11,11,1,11,0 --> D = 0,1,1,1,1,1,11,0,10,10,11
2 distinct digits and 12 terms:
S = 1,1,0,1,0,1,1,0,1,1,11,0 --> D = 0,1,1,1,1,0,1,1,0,10,11
2 distinct digits and 12 terms:
S = 1,1,0,1,0,10,10,0,1,1,11,0 --> D = 0,1,1,1,10,0,10,1,0,10,11
2 distinct digits and 12 terms:
S = 1,1,0,11,1,0,1,1,0,11,11,0 --> D = 0,1,11,10,1,1,0,1,11,0,11
2 distinct digits and 12 terms:
S = 1,1,0,11,11,0,11,11,0,1,11,0 --> D = 0,1,11,0,11,11,0,11,1,10,11
2 distinct digits and 12 terms:
S = 1,1,0,11,11,1,0,1,0,1,11,0 --> D = 0,1,11,0,10,1,1,1,1,10,11
2 distinct digits and 12 terms:
S = 1,1,11,0,11,11,0,11,11,0,1,0 --> D = 0,10,11,11,0,11,11,0,11,1,1
2 distinct digits and 12 terms:
S = 1,1,11,1,0,1,1,0,1,0,1,0 --> D = 0,10,10,1,1,0,1,1,1,1,1
2 distinct digits and 15 terms:
S = 0,1,0,1,0,1,0,1,0,11,11,1,11,1,11 --> D = 1,1,1,1,1,1,1,1,11,0,10,10,10,10
2 distinct digits and 15 terms:
S = 0,1,0,1,0,1,0,1,1,0,1,1,11,1,11 --> D = 1,1,1,1,1,1,1,0,1,1,0,10,10,10

____________________
June 27th update (by Gilles, in French, with an English note at the very end of this page):

Longueurs 6n :

{1,13,32,9,[23,32,9],[41,32,9],12,1} --> {12,19,[23,14,9],[23,32,9],23,3,11}

     N.B.: Il s'agit de ta première solution infiniment extensible.
     Les blocs entre crochets peuvent être échangés, et même combinés
     avec des blocs du premier ordre.

Longueurs 6n + 4 :

{5,54,9,[45,54,9],[63,54,9],4} --> {49,[45,36,9],[45,54,9],45,5}

     Obtenue à partir de l'une des 98 solutions infinies du type de
     la tienne ci-dessus, mais j'ai trouvé peu de bords qui marchent.
     Les blocs entre crochets peuvent encore être échangés,
     et même combinés avec des blocs du premier ordre.

Longueurs 6n + 1 :

{6,45,9,[54,45,9],[54,63,9],54,63,9,3} --> {39,36,45,9,[36,45,9],[54,45,9],54,6}

{4,63,9,[54,63,9],[54,45,9],54,45,9,5} --> {59,54,45,9,[54,45,9],[36,45,9],36,4}

     De nouveau obtenues à partir de deux des 98 solutions infinies.
     Cette fois, l'échange des blocs entre crochets nécessite des
     bords différents, donc il ne sont pas combinables facilement.

Longueurs 6n + 3 :

{0,99,9,[10,11,1,0,99,9]} --> {99,90,[1,1,10,1,99,90]}

Longueurs 6n + 8 :

{2,3,52,9,43,[52,9,43],[34,9,43],34,9,41} --> {1,49,43,[34,9,43],[34,9,25],34,9,25,32}

{3,5,74,9,65,[74,9,65],[56,9,65],56,9,62} --> {2,69,65,[56,9,65],[56,9,47],56,9,47,53}

{4,7,96,9,87,[96,9,87],[78,9,87],78,9,83} --> {3,89,87,[78,9,87],[78,9,69],78,9,69,74} qui illustrent donc tous les 6n + 2, à part 2 qui est impossible.

Longueurs 7n + 4 :

{5,54,9,4,[10,16,6,5,54,9,4]} --> {49,45,5,[6,6,10,1,49,45,5]}

{5,55,0,5,[7,6,12,5,55,0,5]} --> {50,55,5,[2,1,6,7,50,55,5]}

{7,77,0,7,[5,6,12,7,77,0,7]} --> {70,77,7,[2,1,6,5,70,77,7]}

     N.B.: Presque la même greffe que pour {5,55,0,5} !

{9,99,0,9,[42,36,33,9,99,0,9]} --> {90,99,9,[33,6,3,24,90,99,9]}

{1,0,222,21,[24,17,3,1,0,222,21]} --> {1,222,201,[3,7,14,2,1,222,201]}

{10,110,0,1,[10,19,9,10,110,0,1]} --> {100,110,1,[9,9,10,1,100,110,1]}

{10,332,2,3,[14,7,11,10,332,2,3]} --> {322,330,1,[11,7,4,1,322,330,1]}

{10,776,6,7,[88,26,18,10,776,6,7]} --> {766,770,1,[81,62,8,8,766,770,1]}

{20,220,0,2,[6,7,14,20,220,0,2]} --> {200,220,2,[4,1,7,6,200,220,2]}

{20,553,3,5,[77,34,27,20,553,3,5]} --> {533,550,2,[72,43,7,7,533,550,2]}

J'arrête ici les 7n + 4, car il y en a visiblement beaucoup.

Tout de même une généralisation avec des nombres aussi grands qu'on le veut :

{100,1100,0,1,[100,199,99,100,1100,0,1]} --> {1000,1100,1,[99,99,100,1,1000,1100,1]}

{1000,11000,0,1,[1000,1999,999,1000,11000,0,1]} --> {10000,11000,1,[999,999,1000,1,10000,11000,1]}

{10^m,11*10^m,0,1,[10^m,2*10^m-1,10^m-1,10^m,11*10^m,0,1]} --> {10^(m+1),11*10^m,1,[10^m-1,10^m-1,10^m,1,10^(m+1),11*10^m,1]}

Longueurs 8n + 4 :

{10,887,7,8,[9,9,10,1,10,887,7,8]} --> {877,880,1,[1,0,1,9,9,877,880,1]}

{10,887,7,8,[9,11,12,1,10,887,7,8]} --> {877,880,1,[1,2,1,11,9,877,880,1]}

     N.B.: Deux greffes différentes appliquées à la même solution. Ces greffes peuvent être combinées dans un ordre palindrome, par exemple {10,887,7,8,[A],[B],[A]}, où les lettres représentent l'un des crochets ci-dessus.

Longueurs 8n + 5 :

{1,2,22,0,21,[24,17,3,1,2,22,0,21]} --> {1,20,22,21,[3,7,14,2,1,20,22,21]}

     N.B.: On utilise ici la même greffe que pour {1,0,222,21} ci-dessus

{6,30,96,6,42,[33,12,9,6,30,96,6,42]} --> {24,66,90,36,[9,21,3,3,24,66,90,36]}

{7,20,64,4,31,[22,11,9,7,20,64,4,31]} --> {13,44,60,27,[9,11,2,2,13,44,60,27]}

Longueurs 9n + 3 :

{0,11,1,[11,10,11,1,0,1,0,11,1]} --> {11,10,[10,1,1,10,1,1,1,11,10]}

     N.B.: Cette solution est valable en toute base. On peut
     évidemment la multiplier globalement par un chiffre non nul.
     Elle prouve (comme beaucoup d'autres ci-dessous) qu'une chaîne
     faite de 0, 1, 10 & 11 peut être extrêmement longue, alors que mes
     précédentes recherches n'avaient pas dépassé 15 termes.
{0,11,1,[111,110,111,1,0,11,0,11,1]} --> {11,10,[110,1,1,110,1,11,11,11,10]}
{0,11,1,[1111,1110,1111,1,0,111,0,11,1]} --> {11,10,[1110,1,1,1110,1,111,111,11,10]}
{0,11,1,[11...11,11...10,11...11,1,0,1...11,0,11,1]} --> {11,10,[11...10,1,1,11...10,1,1...11,1...11,11,10]}
... où les points de suspension ci-dessus signifient une chaîne aussi longue que l'on veut de 1 répétés. Comme plus haut, toutes ces variantes peuvent être combinées dans un ordre palindrome, par exemple {0,11,1,[A],[B],[C],[B],[A]}.

Longueurs 9n + 5 :

{10,111,1,0,11101,[11100,10100,0,11,10,111,1,0,11101]} --> {101,110,1,11101,[1,1000,10100,11,1,101,110,1,11101]}

Longueurs 9n + 6 :

{0,1,0,11,1,11,[10,11,1,0,1,0,11,1,11]} --> {1,1,11,10,10,[1,1,10,1,1,1,11,10,10]}

{0,11,1,0,1,11,[10,11,1,0,11,1,0,1,11]} --> {11,10,1,1,10,[1,1,10,1,11,10,1,1,10]}

     N.B.: Comme plus haut, c'est valable en toute base,
     et l'on peut multiplier cela par un chiffre non nul.

{0,9,0,9,99,9,[10,11,1,0,9,0,9,99,9]} --> {9,9,9,90,90,[1,1,10,1,9,9,9,90,90]}

{0,9,99,0,9,9,[10,11,1,0,9,99,0,9,9]} --> {9,90,99,9,0,[1,1,10,1,9,90,99,9,0]}

     N.B.: On a utilisé deux fois la même greffe que pour {0,99,9} ci-dessus

{2,9,0,9,99,7,[10,13,3,2,9,0,9,99,7]} --> {7,9,9,90,92,[3,3,10,1,7,9,9,90,92]}

{2,9,99,0,9,7,[10,13,3,2,9,99,0,9,7]} --> {7,90,99,9,2,[3,3,10,1,7,90,99,9,2]}

     N.B.: Même greffe que le précédent

{4,9,0,9,99,5,[10,5,5,4,9,0,9,99,5]} --> {5,9,9,90,94,[5,5,0,1,5,9,9,90,94]}

{4,9,0,9,99,5,[10,15,5,4,9,0,9,99,5]} --> {5,9,9,90,94,[5,5,10,1,5,9,9,90,94]}

     N.B.: Deux greffes différentes pour la même solution {4,9,0,9,99,5}

{4,9,99,0,9,5,[10,5,5,4,9,99,0,9,5]} --> {5,90,99,9,4,[5,5,0,1,5,90,99,9,4]}

{4,9,99,0,9,5,[10,15,5,4,9,99,0,9,5]} --> {5,90,99,9,4,[5,5,10,1,5,90,99,9,4]}

     N.B.: Les mêmes deux greffes sur une variante de la précédente solution

J'arrête ici les 9n + 6, également bien représentés.

Longueurs 10n + 4 :

{1,11,0,1,[0,1,0,10,11,11,1,11,0,1]} --> {10,11,1,[1,1,1,10,1,0,10,10,11,1]}

Longueurs 10n + 5 :

{7,20,64,4,31,[22,10,11,21,9,7,20,64,4,31]} --> {13,44,60,27,[9,12,1,10,12,2,13,44,60,27]}

{11,10,1110,0,111,[111,100,111,11,0,11,10,1110,0,111]} --> {1,1100,1110,111,[0,11,11,100,11,11,1,1100,1110,111]}

Longueurs 10n + 7 :

{11,1,0,1,11,0,1,[0,10,11,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,[1,10,1,0,10,1,1,10,11,1]}

{11,1,0,1,11,0,1,[0,12,11,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,[1,12,1,0,10,1,1,10,11,1]}

     N.B.: Autre greffe possible pour la même solution {11,1,0,1,11,0,1}.

{11,1,11,0,1,0,1,[0,10,11,11,1,11,0,1,0,1]} --> {10,10,11,1,1,1,[1,10,1,0,10,10,11,1,1,1]}

{11,1,11,0,1,0,1,[0,12,11,11,1,11,0,1,0,1]} --> {10,10,11,1,1,1,[1,12,1,0,10,10,11,1,1,1]}

     N.B.: Les mêmes deux greffes sur une variante de la précédente solution. 

Longueurs 11n + 3 :

{0,11,1,[11,10,11,10,111,1,0,1,0,11,1]} --> {11,10,[10,1,1,1,101,110,1,1,1,11,10]}

Longueurs 11n + 5 :

{7,20,64,4,31,[22,11,11,0,11,9,7,20,64,4,31]} --> {13,44,60,27,[9,11,0,11,11,2,2,13,44,60,27]}

Longueurs 12n + 4 :

{1,11,0,1,[0,1,1,0,0,10,10,11,1,11,0,1]} --> {10,11,1,[1,1,0,1,0,10,0,1,10,10,11,1]}

{1,11,0,1,[1,11,10,11,1,0,1,0,1,11,0,1]} --> {10,11,1,[0,10,1,1,10,1,1,1,1,10,11,1]}

Longueurs 12n + 5 :

{1,0,22,2,1,[0,0,1,0,110,111,101,1,0,22,2,1]} --> {1,22,20,1,[1,0,1,1,110,1,10,100,1,22,20,1]}

{2,0,44,4,2,[0,2,1,11,10,11,22,2,0,44,4,2]} --> {2,44,40,2,[2,2,1,10,1,1,11,20,2,44,40,2]}

{2,0,44,4,2,[0,11,0,10,11,11,12,2,0,44,4,2]} --> {2,44,40,2,[2,11,11,10,1,0,1,10,2,44,40,2]}

{2,0,44,4,2,[0,11,0,12,11,11,12,2,0,44,4,2]} --> {2,44,40,2,[2,11,11,12,1,0,1,10,2,44,40,2]}

{24,0,4,44,2,[22,21,10,11,11,0,2,24,0,4,44,2]} --> {24,4,40,42,[20,1,11,1,0,11,2,22,24,4,40,42]}

{24,0,4,44,2,[22,21,11,10,11,0,2,24,0,4,44,2]} --> {24,4,40,42,[20,1,10,1,1,11,2,22,24,4,40,42]}

Longueurs 12n + 6 :

{0,1,0,1,11,1,[11,10,11,1,0,1,0,1,0,1,11,1]} --> {1,1,1,10,10,[10,1,1,10,1,1,1,1,1,1,10,10]}

{0,1,11,0,1,1,[11,10,11,1,0,1,0,1,11,0,1,1]} --> {1,10,11,1,0,[10,1,1,10,1,1,1,1,10,11,1,0]}

Longueurs 12n + 7 :

{11,1,0,1,11,0,1,[1,0,0,10,10,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,0,1,0,10,0,1,10,1,1,10,11,1}

Longueurs 12n + 8 :

{0,0,10,11,1,0,110,10,[11,11,0,1,0,0,10,11,1,0,110,10]} --> {0,10,1,10,1,110,100,[1,0,11,1,1,0,10,1,10,1,110,100]}

Longueurs 12n + 9 :

{0,1,0,1,0,1,11,1,11,[10,11,1,0,1,0,1,0,1,11,1,11]} --> {1,1,1,1,1,10,10,10,[1,1,10,1,1,1,1,1,1,10,10,10]}

{0,1,0,1,11,0,1,1,11,[10,11,1,0,1,0,1,11,0,1,1,11]} --> {1,1,1,10,11,1,0,10,[1,1,10,1,1,1,1,10,11,1,0,10]}

     N.B.: Même greffe sur une variante de la précédente solution

{0,11,1,0,1,1,0,1,11,[10,11,1,0,11,1,0,1,1,0,1,11]} --> {11,10,1,1,0,1,1,10,[1,1,10,1,11,10,1,1,0,1,1,10]}

     N.B.: De nouveau même greffe sur une autre variante des précédentes solutions

Longueurs 13n + 4 :

{1,11,0,1,[0,1,0,10,0,10,10,11,11,1,11,0,1]} --> {10,11,1,[1,1,1,10,10,10,0,1,0,10,10,11,1]}

Longueurs 13n + 7 :

{1,11,1,0,1,0,1,[0,1,0,10,11,11,1,11,1,0,1,0,1]} --> {10,10,1,1,1,1,[1,1,1,10,1,0,10,10,10,1,1,1,1]}

{11,1,0,1,11,0,1,[0,10,0,10,10,11,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,1,10,10,10,0,1,0,10,1,1,10,11,1}

{1,11,0,11,11,0,1,[0,1,0,10,11,11,1,11,0,11,11,0,1]} --> {10,11,11,0,11,1,[1,1,1,10,1,0,10,10,11,11,0,11,1]}

Longueurs 13n + 8 :

{0,0,10,11,1,0,110,10,[11,0,10,11,11,0,0,10,11,1,0,110,10]} --> {0,10,1,10,1,110,100,[1,11,10,1,0,11,0,10,1,10,1,110,100]}

Longueurs 13n + 10 :

{11,1,0,1,0,1,1,11,0,1,[0,10,11,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[1,10,1,0,10,1,1,1,1,0,10,11,1]}

{11,1,0,1,0,1,1,11,0,1,[0,12,11,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[1,12,1,0,10,1,1,1,1,0,10,11,1]}

     N.B.: Mêmes deux greffes possibles que pour les 10n + 7 ci-dessus.

{11,1,11,1,0,1,0,1,0,1,[0,10,11,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[1,10,1,0,10,10,10,1,1,1,1,1,1]}

{11,1,11,1,0,1,0,1,0,1,[0,12,11,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[1,12,1,0,10,10,10,1,1,1,1,1,1]}

     N.B.: Mêmes deux greffes sur une variante de la précédente solution

{11,1,0,11,1,0,11,11,0,1,[0,10,11,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[1,10,1,0,10,1,11,10,1,11,0,11,1]}

{11,1,0,11,1,0,11,11,0,1,[0,12,11,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[1,12,1,0,10,1,11,10,1,11,0,11,1]}

     N.B.: Mêmes deux greffes sur une 2e variante des précédentes solutions

{11,1,0,11,11,0,1,11,0,1,[0,10,11,11,1,0,11,11,0,1,11,0,1]} --> {10,1,11,0,11,1,10,11,1,[1,10,1,0,10,1,11,0,11,1,10,11,1]}

{11,1,0,11,11,0,1,11,0,1,[0,12,11,11,1,0,11,11,0,1,11,0,1]} --> {10,1,11,0,11,1,10,11,1,[1,12,1,0,10,1,11,0,11,1,10,11,1]}

     N.B.: Mêmes deux greffes sur une 3e variante des précédentes solutions

{11,1,11,0,11,11,0,1,0,1,[0,10,11,11,1,11,0,11,11,0,1,0,1]} --> {10,10,11,11,0,11,1,1,1,[1,10,1,0,10,10,11,11,0,11,1,1,1]}

{11,1,11,0,11,11,0,1,0,1,[0,12,11,11,1,11,0,11,11,0,1,0,1]} --> {10,10,11,11,0,11,1,1,1,[1,12,1,0,10,10,11,11,0,11,1,1,1]}

     N.B.: Mêmes deux greffes sur une 4e variante des précédentes solutions

Longueurs 15n + 7 :

{1,11,0,11,11,0,1,[0,1,1,0,0,10,10,11,1,11,0,11,11,0,1]} --> {10,11,11,0,11,1,[1,1,0,1,0,10,0,1,10,10,11,11,0,11,1]}

{1,11,0,11,11,0,1,[1,11,10,11,1,0,1,0,1,11,0,11,11,0,1]} --> {10,11,11,0,11,1,[0,10,1,1,10,1,1,1,1,10,11,11,0,11,1]}

{1,11,1,0,1,0,1,[0,1,1,0,0,10,10,11,1,11,1,0,1,0,1]} --> {10,10,1,1,1,1,[1,1,0,1,0,10,0,1,10,10,10,1,1,1,1]}

{1,11,1,0,1,0,1,[1,11,10,11,1,0,1,0,1,11,1,0,1,0,1]} --> {10,10,1,1,1,1,[0,10,1,1,10,1,1,1,1,10,10,1,1,1,1]}

{11,1,0,1,11,0,1,[0,10,10,11,10,0,1,1,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,1,10,0,1,1,10,1,0,10,10,1,1,10,11,1}

{11,1,0,1,11,0,1,[1,0,0,1,1,0,10,10,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,0,1,0,1,0,1,10,0,1,10,1,1,10,11,1}

{11,1,0,1,11,0,1,[1,0,0,10,10,0,10,10,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,0,1,0,10,0,10,10,0,1,10,1,1,10,11,1}

Longueurs 15n + 8 :

{0,0,10,11,1,0,110,10,[11,1,0,0,10,10,11,0,0,10,11,1,0,110,10]} --> {0,10,1,10,1,110,100,[1,10,1,0,10,0,1,11,0,10,1,10,1,110,100]}

{0,0,10,11,1,0,110,10,[11,11,0,11,11,0,1,0,0,10,11,1,0,110,10]} --> {0,10,1,10,1,110,100,[1,0,11,11,0,11,1,1,0,10,1,10,1,110,100]}

{0,0,10,11,1,0,110,10,[11,11,1,0,1,0,1,0,0,10,11,1,0,110,10]} --> {0,10,1,10,1,110,100,[1,0,10,1,1,1,1,1,0,10,1,10,1,110,100]}

Longueurs 15n + 9 :

{0,1,0,1,0,1,1,11,1,[11,10,11,1,0,1,0,1,0,1,0,1,1,11,1]} --> {1,1,1,1,1,0,10,10,[10,1,1,10,1,1,1,1,1,1,1,1,0,10,10]}

{0,1,0,11,1,0,11,11,1,[11,10,11,1,0,1,0,1,0,11,1,0,11,11,1]} --> {1,1,11,10,1,11,0,10,[10,1,1,10,1,1,1,1,1,11,10,1,11,0,10]}

{0,1,0,11,11,0,1,11,1,[11,10,11,1,0,1,0,1,0,11,11,0,1,11,1]} --> {1,1,11,0,11,1,10,10,[10,1,1,10,1,1,1,1,1,11,0,11,1,10,10]}

{0,1,11,0,11,11,0,1,1,[11,10,11,1,0,1,0,1,11,0,11,11,0,1,1]} --> {1,10,11,11,0,11,1,0,[10,1,1,10,1,1,1,1,10,11,11,0,11,1,0]}

{0,1,11,1,0,1,0,1,1,[11,10,11,1,0,1,0,1,11,1,0,1,0,1,1]} --> {1,10,10,1,1,1,1,0,[10,1,1,10,1,1,1,1,10,10,1,1,1,1,0]}

Longueurs 15n + 10 :

{11,1,0,1,0,1,1,11,0,1,[1,0,0,10,10,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[0,1,0,10,0,1,10,1,1,1,1,0,10,11,1]}

{11,1,0,11,1,0,11,11,0,1,[1,0,0,10,10,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[0,1,0,10,0,1,10,1,11,10,1,11,0,11,1]}

{11,1,11,1,0,1,0,1,0,1,[1,0,0,10,10,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[0,1,0,10,0,1,10,10,10,1,1,1,1,1,1]}

Longueurs 15n + 12 :

{0,1,0,1,0,1,0,1,1,11,1,11,[10,11,1,0,1,0,1,0,1,0,1,1,11,1,11]} --> {1,1,1,1,1,1,1,0,10,10,10,[1,1,10,1,1,1,1,1,1,1,1,0,10,10,10]}

     N.B.: Même greffe que pour 12n + 9 ci-dessus.
     Les sept variantes qui suivent emploient la même greffe.

{0,1,0,1,0,11,1,0,11,11,1,11,[10,11,1,0,1,0,1,0,11,1,0,11,11,1,11]} --> {1,1,1,1,11,10,1,11,0,10,10,[1,1,10,1,1,1,1,1,11,10,1,11,0,10,10]}

{0,1,0,1,0,11,11,0,1,11,1,11,[10,11,1,0,1,0,1,0,11,11,0,1,11,1,11]} --> {1,1,1,1,11,0,11,1,10,10,10,[1,1,10,1,1,1,1,1,11,0,11,1,10,10,10]}

{0,1,0,1,11,0,11,11,0,1,1,11,[10,11,1,0,1,0,1,11,0,11,11,0,1,1,11]} --> {1,1,1,10,11,11,0,11,1,0,10,[1,1,10,1,1,1,1,10,11,11,0,11,1,0,10]}

{0,1,0,1,11,1,0,1,0,1,1,11,[10,11,1,0,1,0,1,11,1,0,1,0,1,1,11]} --> {1,1,1,10,10,1,1,1,1,0,10,[1,1,10,1,1,1,1,10,10,1,1,1,1,0,10]}

{0,11,1,0,1,0,11,11,1,0,1,11,[10,11,1,0,11,1,0,1,0,11,11,1,0,1,11]} --> {11,10,1,1,1,11,0,10,1,1,10,[1,1,10,1,11,10,1,1,1,11,0,10,1,1,10]}

{0,11,1,0,1,1,0,1,1,0,1,11,[10,11,1,0,11,1,0,1,1,0,1,1,0,1,11]} --> {11,10,1,1,0,1,1,0,1,1,10,[1,1,10,1,11,10,1,1,0,1,1,0,1,1,10]}

{0,11,1,0,10,10,0,1,1,0,1,11,[10,11,1,0,11,1,0,10,10,0,1,1,0,1,11]} --> {11,10,1,10,0,10,1,0,1,1,10,[1,1,10,1,11,10,1,10,0,10,1,0,1,1,10]}

Longueurs 16n + 7 :

{1,11,0,11,11,0,1,[0,1,0,10,0,10,10,11,11,1,11,0,11,11,0,1]} --> {10,11,11,0,11,1,[1,1,1,10,10,10,0,1,0,10,10,11,11,0,11,1]}

{1,11,1,0,1,0,1,[0,1,0,10,0,10,10,11,11,1,11,1,0,1,0,1]} --> {10,10,1,1,1,1,[1,1,1,10,10,10,0,1,0,10,10,10,1,1,1,1]}

{11,1,0,1,11,0,1,[0,10,0,1,1,0,10,10,11,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,1,10,10,1,0,1,10,0,1,0,10,1,1,10,11,1}

{11,1,0,1,11,0,1,[0,10,0,10,10,0,10,10,11,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,1,10,10,10,0,10,10,0,1,0,10,1,1,10,11,1}

{11,1,0,1,11,0,1,[1,1,0,1,11,10,11,10,0,11,1,0,1,11,0,1]} --> {10,1,1,10,11,1,0,0,1,1,10,1,1,1,10,11,10,1,1,10,11,1}

Longueurs 16n + 8 :

{0,0,10,11,1,0,110,10,[11,0,10,0,10,10,11,11,0,0,10,11,1,0,110,10} --> {0,10,1,10,1,110,100,[1,11,10,10,10,0,1,0,11,0,10,1,10,1,110,100]}

Longueurs 16n + 10 :

{1,11,1,0,1,1,0,1,0,1,[0,1,0,10,11,11,1,11,1,0,1,1,0,1,0,1]} --> {10,10,1,1,0,1,1,1,1,[1,1,1,10,1,0,10,10,10,1,1,0,1,1,1,1]}

{11,1,0,1,0,1,1,11,0,1,[0,10,0,10,10,11,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[1,10,10,10,0,1,0,10,1,1,1,1,0,10,11,1]}

{11,1,0,11,1,0,11,11,0,1,[0,10,0,10,10,11,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[1,10,10,10,0,1,0,10,1,11,10,1,11,0,11,1]}

{11,1,11,1,0,1,0,1,0,1,[0,10,0,10,10,11,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[1,10,10,10,0,1,0,10,10,10,1,1,1,1,1,1]}

Longueurs 18n + 10 :

{1,11,1,0,1,1,0,1,0,1,[0,1,1,0,0,10,10,11,1,11,1,0,1,1,0,1,0,1]} --> {10,10,1,1,0,1,1,1,1,[1,1,0,1,0,10,0,1,10,10,10,1,1,0,1,1,1,1]}

{1,11,1,0,1,1,0,1,0,1,[1,11,10,11,1,0,1,0,1,11,1,0,1,1,0,1,0,1]} --> {10,10,1,1,0,1,1,1,1,[0,10,1,1,10,1,1,1,1,10,10,1,1,0,1,1,1,1]}

{11,1,0,1,0,1,1,11,0,1,[0,10,10,11,10,0,1,1,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[1,10,0,1,1,10,1,0,10,10,1,1,1,1,0,10,11,1]}

{11,1,0,1,0,1,1,11,0,1,[1,0,0,1,1,0,10,10,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[0,1,0,1,0,1,10,0,1,10,1,1,1,1,0,10,11,1]}

{11,1,0,1,0,1,1,11,0,1,[1,0,0,10,10,0,10,10,11,1,0,1,0,1,1,11,0,1]} --> {10,1,1,1,1,0,10,11,1,[0,1,0,10,0,10,10,0,1,10,1,1,1,1,0,10,11,1]}

{11,1,0,11,1,0,11,11,0,1,[0,10,10,11,10,0,1,1,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[1,10,0,1,1,10,1,0,10,10,1,11,10,1,11,0,11,1]}

{11,1,0,11,1,0,11,11,0,1,[1,0,0,1,1,0,10,10,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[0,1,0,1,0,1,10,0,1,10,1,11,10,1,11,0,11,1]}

{11,1,0,11,1,0,11,11,0,1,[1,0,0,10,10,0,10,10,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[0,1,0,10,0,10,10,0,1,10,1,11,10,1,11,0,11,1]}

{11,1,11,1,0,1,0,1,0,1,[0,10,10,11,10,0,1,1,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[1,10,0,1,1,10,1,0,10,10,10,10,1,1,1,1,1,1]}

{11,1,11,1,0,1,0,1,0,1,[1,0,0,1,1,0,10,10,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[0,1,0,1,0,1,10,0,1,10,10,10,1,1,1,1,1,1]}

{11,1,11,1,0,1,0,1,0,1,[1,0,0,10,10,0,10,10,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[0,1,0,10,0,10,10,0,1,10,10,10,1,1,1,1,1,1]}

Longueurs 18n + 12 :

{0,11,1,0,1,0,11,1,11,10,11,1,[11,10,11,1,0,1,0,11,1,0,1,0,11,1,11,10,11,1]} --> {11,10,1,1,1,11,10,10,1,1,10,[10,1,1,10,1,1,1,11,10,1,1,1,11,10,10,1,1,10]}

{0,11,1,0,11,1,0,1,11,10,11,1,[11,10,11,1,0,1,0,11,1,0,11,1,0,1,11,10,11,1]} --> {11,10,1,11,10,1,1,10,1,1,10,[10,1,1,10,1,1,1,11,10,1,11,10,1,1,10,1,1,10]}

{0,11,1,11,10,11,1,0,1,0,11,1,[11,10,11,1,0,1,0,11,1,11,10,11,1,0,1,0,11,1]} --> {11,10,10,1,1,10,1,1,1,11,10,[10,1,1,10,1,1,1,11,10,10,1,1,10,1,1,1,11,10]}

Longueurs 18n + 15 :

{0,1,0,1,0,1,0,1,1,0,1,1,11,1,11,[10,11,1,0,1,0,1,0,1,0,1,1,0,1,1,11,1,11]} --> {1,1,1,1,1,1,1,0,1,1,0,10,10,10,[1,1,10,1,1,1,1,1,1,1,1,0,1,1,0,10,10,10]}

     N.B.: Même greffe que pour 12n + 9 et 15n + 12 ci-dessus.

{0,1,0,1,0,1,0,1,0,11,11,1,11,1,11,[10,11,1,0,1,0,1,0,1,0,1,0,11,11,1,11,1,11]} --> {1,1,1,1,1,1,1,1,11,0,10,10,10,10,[1,1,10,1,1,1,1,1,1,1,1,1,11,0,10,10,10,10]}

Longueurs 19n + 10 :

{1,11,1,0,1,1,0,1,0,1,[0,1,0,10,0,10,10,11,11,1,11,1,0,1,1,0,1,0,1]} --> {10,10,1,1,0,1,1,1,1,[1,1,1,10,10,10,0,1,0,10,10,10,1,1,0,1,1,1,1]}

{11,1,0,11,1,0,11,11,0,1,[0,10,0,1,1,0,10,10,11,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[1,10,10,1,0,1,10,0,1,0,10,1,11,10,1,11,0,11,1]}

{11,1,0,11,1,0,11,11,0,1,[0,10,0,10,10,0,10,10,11,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[1,10,10,10,0,10,10,0,1,0,10,1,11,10,1,11,0,11,1]}

{11,1,0,11,1,0,11,11,0,1,[1,1,0,1,11,10,11,10,0,11,1,0,11,1,0,11,11,0,1]} --> {10,1,11,10,1,11,0,11,1,[0,0,1,1,10,1,1,1,10,11,10,1,11,10,1,11,0,11,1]}

{11,1,11,1,0,1,0,1,0,1,[0,10,0,1,1,0,10,10,11,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[1,10,10,1,0,1,10,0,1,0,10,10,10,1,1,1,1,1,1]}

{11,1,11,1,0,1,0,1,0,1,[0,10,0,10,10,0,10,10,11,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[1,10,10,10,0,10,10,0,1,0,10,10,10,1,1,1,1,1,1]}

{11,1,11,1,0,1,0,1,0,1,[1,1,0,1,11,10,11,10,0,11,1,11,1,0,1,0,1,0,1]} --> {10,10,10,1,1,1,1,1,1,[0,0,1,1,10,1,1,1,10,11,10,10,10,1,1,1,1,1,1]}

Longueurs (6m+4)(n+1) + 3n :

{5,54,9,[45,54,9],[63,54,9],4,[[10,16,6,5,54,9,[45,54,9],[63,54,9],4]]} --> {49,[45,36,9],[45,54,9],45,5,[[6,6,10,1,49,[45,36,9],[45,54,9],45,5]]}

     N.B.: Même greffe que pour le premier 7n + 4 ci-dessus,
     mais ici appliquée à une solution déjà extensible,
     à savoir la seconde de ce fichier en 6m + 4.

Longueurs (6m+1)(n+1) + 3n :

{6,45,9,[54,45,9],[54,63,9],54,63,9,3,[[10,17,7,6,45,9,[54,45,9],[54,63,9],54,63,9,3]]} --> {39,36,45,9,[36,45,9],[54,45,9],54,6,[[7,7,10,1,39,36,45,9,[36,45,9],[54,45,9],54,6]]}

     N.B.: Greffe de la 3e solution extensible (en 6m + 1)
     donnée en haut de ce fichier.

{4,63,9,[54,63,9],[54,45,9],54,45,9,5,[[10,5,5,4,63,9,[54,63,9],[54,45,9],54,45,9,5]]} --> {59,54,45,9,[54,45,9],[36,45,9],36,4,[[5,5,0,1,59,54,45,9,[54,45,9],[36,45,9],36,4]]}

{4,63,9,[54,63,9],[54,45,9],54,45,9,5,[[10,15,5,4,63,9,[54,63,9],[54,45,9],54,45,9,5]]} --> {59,54,45,9,[54,45,9],[36,45,9],36,4,[[5,5,10,1,59,54,45,9,[54,45,9],[36,45,9],36,4]]}

     N.B.: Deux variantes de greffe appliquées à la 4e solution
     extensible (en 6m + 1) donnée en haut de ce fichier.
     Ces greffes ont déjà été vues pour deux solutions en 9n + 6 ci-dessus.
__________________________________________
English note (by Gilles):
The sequence S may have any number of terms but 2
__________________________________________
Lengths 6n+3 (n ≥ 0):
S = 0,99,9,[10,11,1,0,99,9] --> D = 99,90,[1,1,10,1,99,90]
The segment within square brackets may be repeated several times
Lengths 6n+4 (n ≥ 0):
S = 5,54,9,[45,54,9],[63,54,9],4 --> D = 49,[45,36,9],[45,54,9],45,5
The segments within square brackets may be repeated symmetrically
Lengths 12n+5 (n ≥ 0):
S = 1,0,22,2,1,[0,0,1,0,110,111,101,1,0,22,2,1] --> D = 1,22,20,1,[1,0,1,1,110,1,10,100,1,22,20,1]
Lengths 6n (n ≥ 1):
S = 1,13,32,9,[23,32,9],[41,32,9],12,1 --> D = 12,19,[23,14,9],[23,32,9],23,3,11
Lengths = 6n+1 (n ≥ 1):
S = 4,63,9,[54,63,9],[54,45,9],54,45,9,5 --> D = 59,54,45,9,[54,45,9],[36,45,9],36,4
Lengths 6n+2 (n ≥ 1):
S = 2,3,52,9,43,[52,9,43],[34,9,43],34,9,41 --> D = 1,49,43,[34,9,43],[34,9,25],34,9,25,32
Lengths 12n+11 (n ≥ 0):
S = 5,54,9,[45,54,9],[63,54,9],4,10,16,6,5,54,9,[45,54,9],[63,54,9],4 --> D = 49,[45,36,9],[45,54,9],45,5,6,6,10,1,49,[45,36,9],[45,54,9],45,5
Each segment within square brackets may be repeated the same number of times.
____________________
July 11th update (by Gilles again, in French, with another English note at the very end of the page):

Longueurs 3n (n ≥ 1) :
{[0,111,111],0,11,1} --> {[111,0,111],11,10}
{[0,1110...0,1110...0],0,11,1} --> {[1110...0,0,1110...0],11,10}
Toutes ces variantes peuvent être combinées dans un ordre palindrome, par exemple
{[A],[B],[A],0,11,1} où les lettres représentent l'un des crochets ci-dessus.

Longueurs 3n (n ≥ 2) :
{0,11,[0,1,1],0,1,1,111} --> {11,11,[1,0,1],1,0,110}
{0,11,[1,0,1],1,0,1,11} --> {11,10,[1,1,0],1,1,10}
{0,11,[0,111,111],0,111,111,1} --> {11,11,[111,0,111],111,0,110}
(n = 1 donne une image différente {0,11,1} --> {11,10})

Longueurs 3n + 1 (n ≥ 1) :
{1,[11,0,11],11,0,1} --> {10,[11,11,0],11,1}
{10,[110,0,110],110,0,1} --> {100,[110,110,0],110,1}
{100,[1100,0,1100],1100,0,1} --> {1000,[1100,1100,0],1100,1}
{100...,[1100...,0,1100...],1100...,0,1} --> {1000...,[1100...,1100...,0],1100...,1}

Longueurs 3n + 1 (n ≥ 2):
{1,11,[1,0,1],1,0,1,0,1} --> {10,10,[1,1,0],1,1,1,1}
(n = 1 donne une image différente {1,11,0,1} --> {10,11,1})

[The theorem that S may have any length > 2 is simplified when using these solutions,
as one only needs to quote five cases instead of seven: 3n, 3n+1, 6n+2, 12n+5 and 12n+11.]
____________________
July 12th update: Two new double infinities

Lengths 3*[(m+3)*n + m+2]: S = 0,11,[1,0,1],1,0,1,11,[[10,11,1,0,11,[1,0,1],1,0,1,11]] --> D = 11,10,[1,1,0],1,1,10,[[1,1,10,1,11,10,[1,1,0],1,1,10]]

Lengths (3m+11)*n + 3m+6: S = 0,11,[1,0,1],1,0,1,11,[[10,11,10,111,1,0,11,[1,0,1],1,0,1,11]] --> D = 11,10,[1,1,0],1,1,10,[[1,1,1,101,110,1,11,10,[1,1,0],1,1,10]]

where the segments within single square brackets may be repeated the same number of times (including 0), and the longer ones within double square brackets may be repeated any number of times (including 0).

For n = 1, the second solution gives lengths 6m+17, therefore provides a solution in 6m+5, with m ≥ 2. This allows us to simplify even further the theorem that S may have any number of terms but 2, by using now only four expandable solutions:

Lengths 3n (n ≥ 1): S = [0,111,111],0,11,1 --> D = [111,0,111],11,10
The segment within square brackets may be repeated several times

Lengths 3n+1 (n ≥ 1) : S = 1,[11,0,11],11,0,1 --> D = 10,[11,11,0],11,1

Lengths 6n+5 (n ≥ 2): S = 0,11,[1,0,1],1,0,1,11,10,11,10,111,1,0,11,[1,0,1],1,0,1,11 --> D = 11,10,[1,1,0],1,1,10,1,1,1,101,110,1,11,10,[1,1,0],1,1,1
The segments within square brackets may be repeated the same number of times

Lengths 6n+2 (n ≥ 1): S = 2,3,52,9,43,[52,9,43],[34,9,43],34,9,41 --> D = 1,49,43,[34,9,43],[34,9,25],34,9,25,32
The segments within square brackets may be repeated symmetrically

Since n ≥ 2 is needed for the third solution in 6n+5, we must complement it with two shorter particular cases, for instance

Length 5: S = 1,0,22,2,1 --> D = 1,22,20,1

Length 11:
S = 0,0,1,0,0,10,110,0,10,10,110 --> D = 0,1,1,0,10,100,110,10,0,100





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