A106432 Levenshtein distance between successive powers of 2 in decimal representation.

1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 6, 6, 5, 6, 6, 6, 6, 8, 8, 8, 9, 9, 8, 8, 8, 9, 8, 10, 10, 8, 10, 10, 11, 11, 11, 11, 10, 11, 13, 14, 13, 13, 14, 12, 11, 14, 10, 12, 14, 12, 16, 17, 16, 17, 17, 16, 15, 18, 17, 17, 18, 18, 17, 18, 20, 17, 16, 21, 19, 19, 20, 22, 20, 22, 21

Offset

0,4

Comments

a(n) = minimal number of editing steps (delete, insert or substitute) to transform 2^n into 2^(n+1) in decimal representation;

a(n) <= A034887(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Michael Gilleland, Levenshtein Distance [It has been suggested that this algorithm gives incorrect results sometimes. - N. J. A. Sloane]

Haskell Wiki, Edit distance

WikiBooks: Algorithm Implementation, Levenshtein Distance

Wikipedia, Edit Distance

Wikipedia, Levenshtein Distance

Mathematica

levenshtein[s_List, t_List] := Module[{d, n = Length@s, m = Length@t}, Which[s === t, 0, n == 0, m, m == 0, n, s != t, d = Table[0, {m + 1}, {n + 1}]; d[[1, Range[n + 1]]] = Range[0, n]; d[[Range[m + 1], 1]] = Range[0, m]; Do[ d[[j + 1, i + 1]] = Min[d[[j, i + 1]] + 1, d[[j + 1, i]] + 1, d[[j, i]] + If[ s[[i]] === t[[j]], 0, 1]], {j, m}, {i, n}]; d[[ -1, -1]] ]]; Table[ levenshtein[IntegerDigits[2^n], IntegerDigits[2^(n + 1)]], {n, 0, 80}] (* Robert G. Wilson v *)

Prog

(Haskell)
-- import Data.Function (on)
a106432 n = a106432_list !! n
a106432_list = zipWith (levenshtein `on` show)
                       a000079_list $ tail a000079_list where
   levenshtein us vs = last $ foldl transform [0..length us] vs where
      transform xs@(x:xs') c = scanl compute (x+1) (zip3 us xs xs') where
         compute z (c', x, y) = minimum [y+1, z+1, x + fromEnum (c' /= c)]
-- Reinhard Zumkeller, Nov 10 2013

Crossrefs

Cf. A000079.

Sequence in context: A132944 A210568 A262887 * A227923 A346425 A029836

Adjacent sequences: A106429 A106430 A106431 * A106433 A106434 A106435

Keyword

nonn,base

Author

Reinhard Zumkeller, Jan 22 2006

Extensions

More terms from Robert G. Wilson v, Jan 25 2006

Status

approved