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 A081355 Levenshtein distance between n and n^2 in decimal representation. 6

%I

%S 0,0,1,1,2,1,1,2,2,2,1,1,2,2,2,2,2,3,3,3,2,2,3,2,3,1,2,2,2,3,2,2,3,4,

%T 4,3,3,3,4,4,3,3,4,3,4,3,3,4,4,3,2,3,4,4,4,3,3,4,4,4,2,3,4,3,4,3,3,4,

%U 3,3,3,3,4,3,3,3,2,4,3,4,3,3,3,3,4,3,3,4,4,3,3,3,4,4,4,2,2,3,3,3,2,2,3,3,3

%N Levenshtein distance between n and n^2 in decimal representation.

%H Michael Gilleland, <a href="http://www.merriampark.com/ld.htm">Levenshtein Distance</a>. [It has been suggested that this algorithm gives incorrect results sometimes. - _N. J. A. Sloane_]

%t levenshtein[s_List, t_List] := Module[{d, n = Length@s, m = Length@t}, Which[s === t, 0, n == 0, m, m == 0, n, s != t, d = Table[0, {m + 1}, {n + 1}]; d[[1, Range[n + 1]]] = Range[0, n]; d[[Range[m + 1], 1]] = Range[0, m]; Do[ d[[j + 1, i + 1]] = Min[d[[j, i + 1]] + 1, d[[j + 1, i]] + 1, d[[j, i]] + If[ s[[i]] === t[[j]], 0, 1]], {j, m}, {i, n}]; d[[ -1, -1]] ]];

%t f[n_] := levenshtein[IntegerDigits[n], IntegerDigits[n^2]]; Table[f[n], {n, 0, 104}] (from _Robert G. Wilson v_, Jan 25 2006)

%Y Cf. A081356, A002061, A000290, A081230.

%K nonn,base

%O 0,5

%A _Reinhard Zumkeller_, Mar 18 2003

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