Search: id:A118757
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%I A118757
%S A118757 0,1,2,3,4,5,6,7,8,9,19,18,17,16,15,14,13,12,11,10,20,21,22,23,24,25,26,
%T A118757 27,28,29,39,38,37,36,35,34,33,32,31,30,40,41,42,43,44,45,46,47,48,49,
%U A118757 59,58,57,56,55,54,53,52,51,50,60,61,62,63,64,65,66,67,68,69,79,78,77
%N A118757 Permutation of the natural numbers such that in decimal representation 
               the Levenshtein distance of succeeding terms is exactly 1, a(0)=0.
%C A118757 a(n) = A003100(n) for n<=100, = a(100)=A003100(100)=190, but a(101)=180, 
               A003100(101)=191;
%C A118757 a(n+1) = if U(n) is empty then Min(V(n)) else Max(U(n)), where the sets 
               U and V are defined as: U(m) = {x<a(m): = LD10(a(m),x)=1 and a(k)<>
               x for 0<=k<m}, V(m) = {x>a(m): LD10(a(m),x)=1 and = a(k)<>x for 0<=k<m} 
               with LD10 = Levenshtein distance in decimal representations = of 
               natural numbers;
%C A118757 inverse: A118758; A118759(n)=a(a(n)); a(A118761(n))=A118761(n);
%C A118757 a(n) = A118758(n) for n < 100;
%C A118757 A118762(n) = a(n+1) - a(n).
%H A118757 Michael Gilleland, <a href="http://www.merriampark.com/ld.htm">Levenshtein 
               Distance</a>
%H A118757 R. Zumkeller, <a href="a118757.txt">Initial values of A118757 for n<=1200</
               a>
%H A118757 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%Y A118757 Cf. A118763.
%Y A118757 Sequence in context: A118763 A098488 A003100 this_sequence A118758 A106649 
               A087121
%Y A118757 Adjacent sequences: A118754 A118755 A118756 this_sequence A118758 A118759 
               A118760
%K A118757 nonn,base
%O A118757 0,3
%A A118757 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 01 2006

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