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In ternary representation: minimal number of editing steps (delete, insert or substitute) to transform n into n^2.
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%I #14 May 06 2014 04:13:28

%S 0,0,2,1,1,2,3,2,3,2,2,4,2,4,3,3,4,4,4,4,5,3,4,3,4,3,4,3,3,4,3,3,3,5,

%T 3,5,3,3,5,5,5,6,4,3,4,4,4,5,5,4,4,5,5,5,5,5,6,5,5,5,6,4,5,4,4,5,5,4,

%U 5,4,5,5,5,4,6,4,5,4,5,4,5,4,4,5,4,4,4,5,5,5,4,4,6,4,5,4,4,5,5,5,5,6

%N In ternary representation: minimal number of editing steps (delete, insert or substitute) to transform n into n^2.

%H Robert Israel, <a href="/A091093/b091093.txt">Table of n, a(n) for n = 0..10000</a>

%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_]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Ternary.html">Ternary</a>

%F a(n) = LevenshteinDistance(A007089(n), A001738(n)).

%e a(12)=2: 12->'110', insert a 2 between the 1's and insert a 0 at the end: '12100'->144=12^2.

%p A091093:= proc(x) local L1, L2;

%p L1:= convert(map(`+`,ListTools:-Reverse(convert(x,base,3)),48),bytes);

%p L2:= convert(map(`+`,ListTools:-Reverse(convert(x^2,base,3)),48),bytes);

%p StringTools:-Levenshtein(L1,L2)

%p end proc:

%p seq(A091093(i),i=0..1000); # _Robert Israel_, May 06 2014

%Y Cf. A091092, A091091, A081604, A000290.

%K nonn,base

%O 0,3

%A _Reinhard Zumkeller_, Dec 18 2003