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A322285
Triangle read by rows: T(n,k) is the Damerau-Levenshtein distance between n and k in binary representation, 0 <= k <= n.
3
0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 2, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 3, 3, 2, 3, 1, 2, 2, 3, 0, 3, 3, 2, 2, 1, 1, 2, 2, 1, 0, 3, 3, 2, 2, 1, 1, 1, 2, 1, 1, 0, 3, 3, 2, 2, 2, 1, 2, 1, 2, 1, 1, 0, 3, 3, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 3, 3, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 0
OFFSET
0,7
COMMENTS
The Damerau-Levenshtein distance between two sequences is the number of edit operations (deletions, insertions, substitutions, and adjacent transpositions) needed to transform one into the other.
For consistency with A152487, the binary representation of 0 is assumed to be "0". If instead 0 is represented as the empty sequence, T(n,0) should be increased by 1 for all n except those of the form 2^m-1 for m >= 0.
T(n,k) <= A152487(n,k).
EXAMPLE
The triangle T(n, k) begins:
n\k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
0: 0
1: 1 0
2: 1 1 0
3: 2 1 1 0
4: 2 2 1 2 0
5: 2 2 1 1 1 0
6: 2 2 1 1 1 1 0
7: 3 2 2 1 2 1 1 0
8: 3 3 2 3 1 2 2 3 0
9: 3 3 2 2 1 1 2 2 1 0
10: 3 3 2 2 1 1 1 2 1 1 0
11: 3 3 2 2 2 1 2 1 2 1 1 0
12: 3 3 2 2 1 2 1 2 1 2 1 2 0
13: 3 3 2 2 2 1 1 1 2 1 2 1 1 0
...
The distance between the binary representations of 46 and 25 is 3 (via the edits "101110" - "10111" - "11011" - "11001"), so T(46,25) = 3.
CROSSREFS
Cf. A152487.
Sequence in context: A180918 A152146 A025860 * A152487 A356894 A338019
KEYWORD
nonn,base,tabl
AUTHOR
STATUS
approved