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

0,3

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

Formula

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

Example

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

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

Crossrefs

Cf. A091092, A091091, A081604, A000290.

Sequence in context: A035438 A029260 A205725 * A049615 A114919 A087917

Adjacent sequences: A091090 A091091 A091092 * A091094 A091095 A091096

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 18 2003

Status

approved