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 A152487 Triangle read by rows, 0<=k<=n: T(n,k) = Levenshtein distance of n and k in binary representation. 10
 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, 2, 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, 2, 0, 3, 3, 2, 2, 2, 1, 2, 1, 2, 1, 1, 0, 3, 3, 2, 2, 1, 2, 1, 2, 1, 2, 2, 3, 0, 3, 3, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS T(n,k) gives number of editing steps (replace, delete and insert) to transform n to k in binary representations; row sums give A152488; central terms give A057427; T(n,k) <= Hamming-distance(n,k) for n and k with A070939(n)=A070939(k); T(n,0) = A000523(n+1); T(n,1) = A000523(n) for n>0; T(n,3) = A106348(n-2) for n>2; T(n,n-1) = A091090(n-1) for n>0; T(n,n) = A000004(n); T(A000290(n),n) = A091092(n). T(n,k) >= A322285(n,k) - Pontus von Brömssen, Dec 02 2018 LINKS Alois P. Heinz, Rows n = 0..200, flattened Michael Gilleland, Levenshtein Distance Wikipedia, Levenshtein Distance FORMULA T(n,k) = f(n,k) with f(x,y) = if x>y then f(y,x) else if x<=1 then Log2(y)-0^y+(1-x)*0^(y+1-2^(y+1)) else Min{f([x/2],[y/2]) + (x mod 2) XOR (y mod 2), f([x/2],y)+1, f(x,[y/2])+1}, where Log2=A000523. 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  2  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  2  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  2  3  0   13:  3  3  2  2  2  1  1  1  2  1  2  2  1  0   ... The distance between the binary representations of 46 and 25 is 4 (via the edits "101110" - "10111" - "10011" - "11011" - "11001"), so T(46,25) = 4. - Pontus von Brömssen, Dec 02 2018 CROSSREFS Cf. A000004, A000290, A000523, A057427, A070939, A091090, A091092, A106348, A152488, A322285. Sequence in context: A152146 A025860 A322285 * A058394 A122860 A113661 Adjacent sequences:  A152484 A152485 A152486 * A152488 A152489 A152490 KEYWORD nonn,base,tabl AUTHOR Reinhard Zumkeller, Dec 06 2008 STATUS approved

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)