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.

1, 0, 11, 15, 111, 121, 1011, 1111, 2011, 11111, 16111, 111111, 131011, 1011111, 1111111, 2011111, 11111111, 16111111, 111111111, 131111111, 1011111111, 1111111111, 2111111111, 11111111111

Offset

0,3

Comments

Difference between A115779&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..23.

Formula

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

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[ t[[f@n+1]] = n, {n, 10^6}]; t

Crossrefs

Cf. A000027, A007088, A115777.

Sequence in context: A219389 A217085 A267123 * A147339 A147377 A147333

Adjacent sequences: A115776 A115777 A115778 * A115780 A115781 A115782

Keyword

more,nonn,base

Author

Robert G. Wilson v, Jan 26 2006

Extensions

a(18)-a(23) from Lars Blomberg, Jul 16 2015

Status

approved