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

Author

Reinhard Zumkeller, Dec 18 2003

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• 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

Crossrefs

Cf. A091093, A091091, A070939, A000290.

Formula

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