Slide my digits and divide

Three sequences with sliding divider-digits

A. Lexicographically earliest sequence of distinct positive terms such that any digit “d” sliding “d” terms to the right divides the last term of the slip – except for the digit 0 that does not move and does nothing.
B. Lexicographically earliest sequence of distinct nonnegative terms such that any digit “d” sliding “d” terms to the left divides the last term of the slip – except for the digit 0 that does not move and does nothing
C. Lexicographically earliest sequence of distinct nonnegative terms such that any digit “d” sliding “d” terms either to the right or to the left divides the last term of the slip – except for the digit 0 that does not move and does nothing.

A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …

Check
The 1st digit of A is 1, slides 1 term to the right and divides the term 2:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 2, slides 2 terms to the right and divides the term 4:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 3, slides 3 terms to the right and divides the term 6:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 4, slides 4 terms to the right and divides the term 8:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 5, slides 5 terms to the right and divides the term 10:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
…
The hereunder yellow digit 8 slides 8 terms to the right and divides the term 24:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 9, slides 9 terms to the right and divides the term 36:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 1, slides 1 term to the right and divides the term 11:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 0, which does not move and does nothing:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 1, slides 1 term to the right and divides the term 12:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 1, slides 1 term to the right and also divides the term 12:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 1, slides 1 term to the right and divides the term 13:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 2, slides 2 terms to the right and divides the term 14:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 1, slides 1 term to the right and also divides the term 14:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 3, slides 3 terms to the right and divides the term 24:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 1, slides 1 term to the right and divides the term 15:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
The next digit is 4, slides 4 terms to the right and divides the term 36:
A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, …
Etc.
______________________________

B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …

Check
The 1st digit of B is 0, which does not move and does nothing:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 0:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 2, slides 2 terms to the left and also divides the term 0:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 3, slides 3 terms to the left and also divides the term 0:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
…
The hereunder yellow digit 1 slides 1 term to the left and divides the term 9:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 0, which does not move and does nothing:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 10:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and also divides the term 10:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 11:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 2, slides 2 terms to the left and also divides the term 10:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 12:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next two digits are 0s and we leave them in peace:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 100:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 7, slides 7 terms to the left and divides the term 7:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 17:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 3, slides 3 terms to the left and divides the term 12:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 1, slides 1 term to the left and divides the term 13:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 4, slides 4 terms to the left and also divides the term 12:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
The next digit is 4, slides 4 terms to the left and divides the term 100:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
…
The hereunder yellow digit 8 slides 8 terms to the left and divides the term 40:
B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 17, 13, 14, 40, 15, 20, 101, 21, 50, 41, 22, 18, 102, 25, 23, 30, …
Etc.
(work in progress)
(going to bed now – hoping I did not leave too many mistakes above)
(will compute by hand the seq C tomorrow)

____________________
Next morning update
Jean-Marc Falcoz was quick to extend A and B and send the according (beautiful) graphs::

A = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,24,16,36,17,20,18,22,30,42,19,84,21,28,32,40,26,27,34,72,23,48,60,33,35,44,63,39,54,120,45,38,96,25,108,50,81,29,90,56,55,99,64,31,80,150,144,117,66,37,180,41,168,43,126,52,210,68,192,46,240,47,58,132,76,216,51,270,49,62,264,420,88,70,112,156,78,135,53,57,840,102,65,140,160,59,77,100,288,61,300,67,69,105,153,114,104,138,630,200,204,162,74,82,228,128,92,174,86,91,71,136,152,176,252,171,184,1050,189,330,196,73,315,75,312,87,336,225,175,198,98,79,1260,280,94,154,83,208,504,324,360,224,276,540,232,248,186,348,390,308,93,372,222,384,408,256,111,432,364,234,165,456,480,116,246,220,600,258,124,282,528,106,660,85,89,320,95,552,720,110,118,400,440,207,97,756,148,101,272,103,560,294,147,306,296,700,396,107,109,378,342,113,462,243,588,414,672,576,318,260,115,354,960,546,231,780,520,444,450,366,119,900,...

A – 10000 terms

B = 0,1,2,3,4,5,6,7,8,9,10,11,12,100,17,13,14,40,15,20,101,21,50,41,22,18,102,25,23,30,110,16,26,111,19,44,31,112,1000,24,120,42,32,33,27,51,34,36,28,121,38,104,114,29,122,37,90,1001,60,80,200,35,46,45,47,55,53,81,57,1010,103,113,91,1011,105,1100,39,123,1101,43,115,70,1110,201,202,130,52,125,61,1111,54,10000,150,131,210,133,56,135,62,58,63,71,75,73,88,300,92,72,124,49,132,64,48,66,140,82,67,211,106,65,108,77,212,301,141,10001,116,303,107,99,74,10010,203,220,10011,221,151,134,59,117,10100,10101,213,10110,143,152,310,222,79,126,311,155,313,68,10111,...
B – 1000 terms

C = 0,1,2,3,4,5,6,7,8,9,10,11,12,100,70,13,24,14,90,15,20,700,16,21,25,40,30,99,210,300,18,22,33,28,50,36,126,41,120,35,72,336,42,17,60,19,68,630,26,27,420,110,102,66,144,23,56,130,96,162,111,200,48,32,108,114,84,234,29,80,168,88,112,31,104,44,192,288,128,184,34,101,46,444,180,1008,208,224,132,52,62,204,240,248,160,124,1020,64,106,140,222,152,82,312,150,118,270,43,122,55,216,188,116,1120,45,92,414,134,228,320,720,212,246,94,54,39,600,308,360,190,141,51,666,53,252,1000,810,91,1260,310,156,37,201,38,456,170,612,93,1204,330,264,1112,840,202,220,74,1044,105,61,380,304,121,525,1014,504,103,113,3000,408,660,63,47,148,69,65,816,384,71,133,390,1104,606,261,232,448,76,621,402,1080,142,123,372,1848,516,213,49,344,303,1610,1116,432,211,172,354,828,276,306,332,230,294,1002,426,2016,292,302,136,146,462,1026,174,280,900,1332,888,324,135,154,117,480,161,1620,800,244,57,196,450,528,221,340,808,1050,1110,164,153,328,115,540,768,1140,131,400,145,624,510,616,352,440,1010,1200,166,1440,73,58,81,468,1500,83,1030,1148,129,1560,1016,392,109,424,75,1224,10110,1188,77,500,333,441,601,138,95,2072,309,1012,1170,690,119,1024,301,522,151,12600,311,272,3330,1710,125,342,370,158,231,1680,10010,159,290,1001,250,576,710,512,203,410,7110,1062,2100,812,322,78,206,546,226,79,702,176,21000,1032,1122,214,1134,1302,6111,396,636,181,321,147,474,366,1206,912,2232,1232,266,1344,642,241,1212,348,1728,236,672,284,1146,242,260,3024,1128,1092,186,520,1230,262,602,282,960,502,2160,318,1242,67,1320,5000,1068,603,86,1944,315,191,618,804,2112,155,920,388,990,169,2520,544,182,205,218,5040,610,171,225,404,10000,163,1272,580,924,215,194,930,460,1022,1380,712,412,1152,1404,1422,1476,314,1400,268,1164,608,492,245,904,714,648,10200,560,832,472,1602,588,2250,1248,98,238,3360,620,177,696,401,488,1056,4104,820,2436,334,880,1314,552,1028,438,592,411,1410,680,143,860,11000,1512,256,2124,254,1488,430,640,708,1800,892,316,350,1824,165,882,13000,2040,992,2070,1434,416,107,1632,508,428,861,2142,149,4200,313,1088,30000,744,752,243,274,1548,1236,1160,1288,1428,1040,406,534,2400,940,732,728,4440,564,251,223,364,1540,10710,2280,484,1004,1350,127,452,1176,1100,1280,464,1210,1141,594,4004,281,2052,1808,1180,137,421,470,1494,1520,1220,928,5152,422,2240,442,1042,1980,1124,872,2088,704,524,233,1102,1144,12096,1880,2128,824,1114,1142,654,724,1108,792,1208,1240,1266,1202,1414,436,11200,801,1296,844,434,570,1011,1704,1308,1312,85,936,4011,446,1113,185,100000,1368,2000,780,1530,157,323,1416,518,2880,910,1424,1211,1290,550,476,2032,1072,590,2700,1021,2004,17010,1150,385,368,10101,1125,195,770,331,972,15000,5280,235,1034,490,405,1155,1060,1908,1328,255,530,1554,774,219,305,31000,9000,1101,207,455,454,59,1161,1888,1580,13230,1070,494,2010,505,2502,536,1712,511,1590,4000,2610, ...

Thank you, Jean-Marc – this is a marvel (three marvels!-)
















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