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A115779 Consider the Levenshtein distance between k considered as a decimal string and k considered as a binary string. Then a(n) is the greatest number m such that the Levenshtein distance is n or 0 if no such number exists.

%I A115779 #10 Jul 16 2015 09:39:25
%S A115779 1,0,11,15,111,121,1011,1111,2011,11111,16111,111111,131011,1011111,
%T A115779 1111111,2011111,11111111,16111111,111111111,131111111,1011111111,
%U A115779 1111111111,2111111111,11111111111
%N A115779 Consider the Levenshtein distance between k considered as a decimal string and k considered as a binary string. Then a(n) is the greatest number m such that the Levenshtein distance is n or 0 if no such number exists.
%C A115779 Difference between A115779&A115778: 1, 0, 9, 11, 103, 99, 979, 1047, 1789, 10855, 15599, 109067, 128789, 1006889, 1102919, 1988889, 11078343, ...,.
%F A115779 a(1)=0 since no number satisfies the definition and generally a(n)>= 2^(n+1).
%t A115779 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 A115779 t = Table[0, {25}]; f[n_] := levenshtein[ IntegerDigits[n], IntegerDigits[n, 2]]; Do[ t[[f@n+1]] = n, {n, 10^6}]; t
%Y A115779 Cf. A000027, A007088, A115777.
%K A115779 more,nonn,base
%O A115779 0,3
%A A115779 _Robert G. Wilson v_, Jan 26 2006
%E A115779 a(18)-a(23) from _Lars Blomberg_, Jul 16 2015