

A109382


Levenshtein distance between successive English names of nonnegative integers, excluding spaces and hyphens.


3



4, 3, 4, 5, 3, 3, 4, 5, 4, 3, 4, 4, 6, 3, 3, 2, 4, 4, 3, 7, 3, 3, 4, 5, 3, 3, 4, 5, 4, 7, 3, 3, 4, 5, 3, 3, 4, 5, 4, 7, 3, 3, 4, 5, 3, 3, 4, 5, 4, 6, 3, 3, 4, 5, 3, 3, 4, 5, 4, 6, 3, 3, 4, 5, 3, 3, 4, 5, 4, 7, 3, 3, 4, 5, 3, 3, 4, 5, 4, 8, 3, 3, 4, 5, 3, 3, 4, 5, 4, 7, 3, 3, 4, 5, 3, 3, 4, 5, 4, 7, 3, 3, 4, 5, 3, 3
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OFFSET

0,1


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
Michael Gilleland, Levenshtein Distance, in Three Flavors.
V. I. Levenshtein, Efficient reconstruction of sequences from their subsequences or supersequences, J. Combin. Theory Ser. A 93 (2001), no. 2, 310332.
Landon Curt Noll, The English Name of a Number.
Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens.


FORMULA

a(n) = LD(nameof(n), nameof(n+1)).


EXAMPLE

a(0) = 4 since LD(ZERO,ONE) requires 4 edits.
a(1) = 3 since LD(ONE,TWO) which requires 3 substitutions.
a(2) = 4 since LD(TWO,THREE) = requires 4 edits (leave the leftmost T unchanged), then 2 substitutions (W to H, O to R), then 2 insertions (E,E).
a(4) = 3 as LD(FOUR,FIVE) leaves the leftmost F unchanged, then requires 3 substitutions. From FIVE to SIX leaves the I unchanged. From SIX to SEVEN leaves the S unchanged. From TEN to ELEVEN leaves the EN unchanged. From ELEVEN to TWELVE leaves an E,L,V,E unchanged. From THIRTEEN to FOURTEEN leaves RTEEN unchanged. TWENTYNINE to THIRTY takes 7 edits. THIRTYNINE to FORTY takes 7 edits. SEVENTYNINE to EIGHTY takes 8 edits. EIGHTYNINE to NINETY takes 7 edits. NINETYNINE to ONEHUNDRED takes 7 edits.


MAPLE

with(StringTools):
seq(Levenshtein(Select(IsAlpha, convert(n, english)), Select(IsAlpha, convert(n+1, english))), n=0..200); # Robert Israel, Jan 23 2018


MATHEMATICA

(* First copy b109382.txt out of A109382 then *) 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]] ]]; f[x_] := Block[{str = ToString@ lst[[x]], len}, len = StringLength@ str; StringInsert[str, ", ", Range[2, len]]]


CROSSREFS

Cf. A001477, A005589, A081355, A081356, A081230, A109809, A109811.
Sequence in context: A204818 A099634 A203144 * A090369 A260031 A132293
Adjacent sequences: A109379 A109380 A109381 * A109383 A109384 A109385


KEYWORD

easy,nonn,word


AUTHOR

Jonathan Vos Post, Aug 25 2005


EXTENSIONS

More terms from Robert G. Wilson v, Jan 31 2006
Corrected by Robert Israel, Jan 23 2018


STATUS

approved



