A367638 Sequence S of positive integers such that the successive digits d of S are the successive Levenshtein distances between two adjacent terms of S. When possible, S is always extended with the smallest positive integer not yet present.

1, 2, 10, 11, 11, 12, 13, 3, 4, 5, 14, 15, 200, 6, 1000, 22111, 2111, 7, 8, 10000, 100, 100, 100, 222211, 22211, 22211, 22211, 22211, 211, 16, 17, 18, 19, 20, 21, 22, 23, 1000000, 22111111, 2111111, 2111111, 2111111, 2111111, 2111111, 111111, 111111, 111111, 11111, 11111, 11111, 1111, 1111, 1111, 101, 30, 9, 24

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Éric Angelini, A sequence with Vladimir Iosifovich (and his wife), Personal blog, Nov 2023.

Example

The sequence starts with 1, 2, 10, 11, 11, 12, 13, 3.
a(1) = 1 is indeed the Ld (Levenshtein distance) between a(1) = 1 and a(2) = 2;
a(2) = 2 is the Ld between a(2) = 2 and a(3) = 10;
a(3) = 10 whose first digit 1 is the Ld between a(3) = 10 and a(4) = 11;
a(3) = 10 whose second digit 0 is the Ld between a(4) = 11 and a(5) = 11;
a(4) = 11 whose first digit 1 is the Ld between a(5) = 11 and a(6) = 12;
a(4) = 11 whose second digit 1 is the Ld between a(6) = 12 and a(7) = 13;
a(5) = 11 whose first digit 1 is the Ld between a(7) = 13 and a(8) = 3; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=If[Flatten[IntegerDigits/@(ar=Array[a, n-1])][[n-1]]==0, a[n-1], (k=1; While[MemberQ[ar, k]||EditDistance[ToString@a[n-1], ToString@k]!=Flatten[IntegerDigits/@Join[ar, {k}]][[n-1]], k++]; k)]; Array[a, 23]

Crossrefs

Cf. A118757, A151875.

Sequence in context: A338401 A222638 A299982 * A089601 A171893 A278816

Adjacent sequences: A367635 A367636 A367637 * A367639 A367640 A367641

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Nov 25 2023

Status

approved