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A115778 Consider the Levenshtein distance between k considered as a decimal string and k considered as a binary string. Then a(n) is the least number m such that the Levenshtein distance is n or 0 if no such number exists. 3
1, 0, 2, 4, 8, 22, 32, 64, 222, 256, 512, 2044, 2222, 4222, 8192, 22222, 32768, 65536, 222222, 262144, 524288, 2097152, 2222222, 4194322, 8388622, 22222222, 33554432, 67222222, 222222222, 268435456, 536872222, 2147483650, 2147483648, 4294967296, 8589934592, 22222222222 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Difference between A115779 and A115778: 1, 0, 9, 11, 103, 99, 979, 1047, 1789, 10855, 15599, 109067, 128789, 1006889, 1102919, 1988889, 11078343, ...,.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(1)=0 since no number satisfies the definition and generally a(n)>= 2^(n+1).

MAPLE

f:= n -> StringTools:-Levenshtein(convert(n, string), convert(convert(n, binary), string)):

A:= Vector(20):

for n from 3 to 10^6 do

  v:= f(n);

  if A[v] = 0 then A[v]:= n fi

od:

1, 0, seq(A[n], n=2..20); # Robert Israel, Jul 16 2015

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]]]];

t = Table[0, {25}]; f[n_] := levenshtein[ IntegerDigits[n], IntegerDigits[n, 2]]; Do[a = f[n]; If[ t[[a+1]] == 0, t[[a+1]] = n; Print[{a, n}]], {n, 10^6}]; t

CROSSREFS

Cf. A000027, A007088, A115777.

Sequence in context: A133604 A262345 A192149 * A333016 A295628 A027713

Adjacent sequences:  A115775 A115776 A115777 * A115779 A115780 A115781

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Jan 26 2006

EXTENSIONS

a(26)-a(35) from Lars Blomberg, Jul 16 2015

STATUS

approved

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Last modified September 23 15:23 EDT 2021. Contains 347618 sequences. (Running on oeis4.)