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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.

%I A322285 #22 Oct 09 2019 13:35:42
%S A322285 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,
%T A322285 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,
%U A322285 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
%N A322285 Triangle read by rows: T(n,k) is the Damerau-Levenshtein distance between n and k in binary representation, 0 <= k <= n.
%C A322285 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.
%C A322285 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.
%C A322285 T(n,k) <= A152487(n,k).
%H A322285 Pontus von Brömssen, <a href="/A322285/b322285.txt">Rows n = 0..200, flattened</a>
%H A322285 Wikipedia, <a href="https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance">Damerau-Levenshtein distance</a>
%H A322285 <a href="http://oeis.org/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A322285 The triangle T(n, k) begins:
%e A322285   n\k  0  1  2  3  4  5  6  7  8  9 10 11 12 13 ...
%e A322285    0:  0
%e A322285    1:  1  0
%e A322285    2:  1  1  0
%e A322285    3:  2  1  1  0
%e A322285    4:  2  2  1  2  0
%e A322285    5:  2  2  1  1  1  0
%e A322285    6:  2  2  1  1  1  1  0
%e A322285    7:  3  2  2  1  2  1  1  0
%e A322285    8:  3  3  2  3  1  2  2  3  0
%e A322285    9:  3  3  2  2  1  1  2  2  1  0
%e A322285   10:  3  3  2  2  1  1  1  2  1  1  0
%e A322285   11:  3  3  2  2  2  1  2  1  2  1  1  0
%e A322285   12:  3  3  2  2  1  2  1  2  1  2  1  2  0
%e A322285   13:  3  3  2  2  2  1  1  1  2  1  2  1  1  0
%e A322285   ...
%e A322285 The distance between the binary representations of 46 and 25 is 3 (via the edits "101110" - "10111" - "11011" - "11001"), so T(46,25) = 3.
%Y A322285 Cf. A152487.
%K A322285 nonn,base,tabl
%O A322285 0,7
%A A322285 _Pontus von Brömssen_, Dec 02 2018