A091093 In ternary representation: minimal number of editing steps (delete, insert or substitute) to transform n into n^2.

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Dec 18 2003

Keywords

• nonn
• base

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Michael Gilleland, Levenshtein Distance [It has been suggested that this algorithm gives incorrect results sometimes. - _N. J. A. Sloane_]
• Eric Weisstein's World of Mathematics, Square Number
• Eric Weisstein's World of Mathematics, Ternary

Crossrefs

Cf. A091092, A091091, A081604, A000290.

Programs

Maple

A091093:= proc(x) local L1, L2;
   L1:= convert(map(`+`,ListTools:-Reverse(convert(x,base,3)),48),bytes);
   L2:= convert(map(`+`,ListTools:-Reverse(convert(x^2,base,3)),48),bytes);
   StringTools:-Levenshtein(L1,L2)
end proc:
seq(A091093(i),i=0..1000); # Robert Israel, May 06 2014

Formula

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