A091091 -id:A091091 - cp's OEIS frontend

A091092 In binary representation: minimal number of editing steps (delete, insert or substitute) to transform n into n^2.

0, 0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 6, 6, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 7, 8, 8, 7, 8, 8, 7, 7, 7, 7, 7, 8

Offset: 0

Reinhard Zumkeller, Dec 18 2003

a(n) = A152487(A000290(n),n). - Reinhard Zumkeller, Dec 06 2008

			a(7)=3: 7->'111', 3 x insert a 0 between the last two 1's:
'110001'->49=7^2.

Alois P. Heinz, Table of n, a(n) for n = 0..20000
Eric Weisstein's World of Mathematics, Square Number
Eric Weisstein's World of Mathematics, Binary
Wikipedia, Levenshtein Distance
Index entries for sequences related to binary expansion of n

Cf. A091093, A091091, A070939, A000290.

a(n) = LevenshteinDistance(A007088(n), A001737(n)).

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

Original entry on oeis.org

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

Reinhard Zumkeller, Dec 18 2003

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

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

Cf. A091092, A091091, A081604, A000290.

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

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

cp's OEIS Frontend

A091092 In binary representation: minimal number of editing steps (delete, insert or substitute) to transform n into n^2.

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