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 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 (list; graph; refs; listen; history; text; internal format)
 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, 310-332. 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,changed 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

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Last modified December 10 10:58 EST 2018. Contains 318047 sequences. (Running on oeis4.)