More Levenshtein distances

(Dall.e creation)

New ideas about the Levenshtein distances? Giorgos Kalogeropoulos computed the hereunder seqs – many thanks to him!

[A] «Lexico-earliest seq A of distinct positive terms not ending in 0 such that the Levenshtein distance between a(n) and a(n+1) is equal to the last digit of a(n)»
A = 1, 2, 11, 12, 3, 101, 102, 13, 201, 21, 22, 4, 1001, 1002, 103, 5, 10001, 10002, 1003, 14, 2001, 2002, 203, 6, 100001, 100002, 10003, 104, 2211, 211, 111, 112, 15, 20001, 20002, 202, 23, 105, 22211, 2221, 221, 121, 122, 16, 200001, 200002, 20003, 204, 1111, 1011, 1012, 106, 222211, 22221, 2222, 212, 17....

[B] «Lexico-earliest seq B of distinct positive terms such that the Levenshtein distance between a(n) and a(n+1) is equal to the first digit of a(n+1)»
B = 1, 10, 2, 12, 11, 13, 14, 15, 16, 17, 18, 19, 20, 120, 3, 21, 121, 22, 122, 23, 123, 24, 124, 25, 125, 26, 126, 27, 127, 28, 128, 29, 129, 30, 130, 100, 31, 131, 101, 32, 132, 102, 33, 133, 103, 34, 134, 104, 35, 135, 105, 36, 136, 106, 37, 137, 107, 38, 138, 108, 39, 139, 109, 119, 110, 111, 112, 113, 114, 115, 116, 117, 118, 148, 140, 141, 142, 143, 144, 145, 146, 147, 149, 159, 150, 151, 152, 153, 154, 155, 156, 157, 158, 168, 160, 161, 162, 163, 164, 165, ...

[C] «Lexico-earliest seq C of distinct nonnegative terms such that the Levenshtein distance between a(n) and a(n+1) is equal to 1»
C = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 10, 11, 12, 13, 14, 15, 16, 17, 18, 28, 20,...
(this has already been studied in A118763)

[D] «Lexico-earliest seq D of distinct nonnegative terms such that the Levenshtein distance between a(n) and a(n+1) is equal to 2»
D = 0, 11, 2, 10, 3, 12, 4, 13, 5, 14, 6, 15, 7, 16, 8, 17, 9, 18, 20, 1, 22, 19, 21, 30, 23, 31, 24, 32, 25, 33, 26, 34, 27, 35, 28, 36, 29, 37, 40, 38, 41, 39, 42, 50, 43, 51, 44, 52, 45, 53, 46, 54, 47, 55, 48, 56, 49, 57, 60, 58, 61, 59, 62, 70, 63, 71, 64, 72, 65, 73, 66, 74, 67, 75, 68, 76, 69, 77, 80, 78, 81, 79, 82, 90, 83, 91, 84, 92, 85, 93, 86, 94, 87, 95, 88, 96, 89, 97, 107, 110,...

[E] «Lexico-earliest seq E of distinct nonnegative terms such that the Levenshtein distance between a(n) and a(n+1) is equal to 3»
E = 0, 111, 2, 100, 3, 101, 4, 102, 5, 103, 6, 104, 7, 105, 8, 106, 9, 107, 21, 108, 22, 109, 23, 110, 24, 112, 20, 113, 25, 114, 26, 115, 27, 116, 28, 117, 29, 118, 30, 119, 32, 140, 31, 120, 33, 121, 34, 122, 35, 123, 36, 124, 37, 125, 38, 126, 39, 127, 40, 128, 41, 129, 43, 150, 42, 130, 44, 131, 45, 132, 46, 133, 47, 134, 48, 135, 49, 136, 50, 137, 51, 138, 52, 139, 54, 160, 53, 141, 55, 142, 56, 143, 57, 144, 58, 145, 59, 146, 60, 147,...

[F] «Lexico-earliest seq F of distinct nonnegative terms such that the Levenshtein distance between a(n) and a(n+1) is equal to 4»
F = 0, 1111, 2, 1000, 3, 1001, 4, 1002, 5, 1003, 6, 1004, 7, 1005, 8, 1006, 9, 1007, 21, 1008, 22, 1009, 23, 1010, 24, 1011, 25, 1012, 26, 1013, 27, 1014, 28, 1015, 29, 1016, 32, 1017, 33, 1018, 34, 1019, 35, 1020, 31, 1022, 36, 1021, 37, 1023, 38, 1024, 39, 1025, 41, 1026, 43, 1027, 44, 1028, 45, 1029, 46, 1030, 42, 1031, 47, 1032, 48, 1033, 49, 1034, 51, 1035, 52, 1036, 54, 1037, 55, 1038, 56, 1039, 57, 1040, 53, 1041, 58, 1042, 59, 1043, 61, 1044, 62, 1045, 63, 1046, 65, 1047, 66, 1048,...

[G] «Lexico-earliest seq G of distinct nonnegative terms such that the Levenshtein distance between a(n) and a(n+1) is equal to 5»
G = 0, 11111, 2, 10000, 3, 10001, 4, 10002, 5, 10003, 6, 10004, 7, 10005, 8, 10006, 9, 10007, 21, 10008, 22, 10009, 23, 10010, 24, 10011, 25, 10012, 26, 10013, 27, 10014, 28, 10015, 29, 10016, 32, 10017, 33, 10018, 34, 10019, 35, 10020, 31, 10022, 36, 10021, 37, 10023, 38, 10024, 39, 10025, 41, 10026, 43, 10027, 44, 10028, 45, 10029, 46, 10030, 42, 10031, 47, 10032, 48, 10033, 49, 10034, 51, 10035, 52, 10036, 54, 10037, 55, 10038, 56, 10039, 57, 10040, 53, 10041, 58, 10042, 59, 10043, 61, 10044, 62, 10045, 63, 10046, 65, 10047, 66, 10048,...

GK
> the pattern continues with bigger numbers.
EA
Bravo and thanks Giorgos!
Those seqs will be published soon by the OEIS.





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