cp's OEIS Frontend

A367813 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 3.

%I A367813 #11 Dec 21 2023 15:17:10
%S A367813 0,111,2,100,3,101,4,102,5,103,6,104,7,105,8,106,9,107,21,108,22,109,
%T A367813 23,110,24,112,20,113,25,114,26,115,27,116,28,117,29,118,30,119,32,
%U A367813 140,31,120,33,121,34,122,35,123,36,124,37,125,38,126,39,127,40,128,41,129,43,150,42,130,44,131,45,132,46,133
%N A367813 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 3.
%H A367813 Éric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/12/more-levenshtein-distances.html">More Levenshtein distances</a>, Personal blog, December 2023.
%e A367813 a(1) =   0 and a(2) = 111 are separated by a Ld of 3
%e A367813 a(2) = 111 and a(3) =   2 are separated by a Ld of 3
%e A367813 a(3) =   2 and a(4) = 100 are separated by a Ld of 3
%e A367813 a(4) = 100 and a(5) =   3 are separated by a Ld of 3, etc.
%t A367813 a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=3,k++];k);Array[a,72]
%o A367813 (Python)
%o A367813 from itertools import islice
%o A367813 from Levenshtein import distance as Ld
%o A367813 def agen(): # generator of terms
%o A367813     an, aset, mink = 0, {0}, 1
%o A367813     while True:
%o A367813         yield an
%o A367813         s, k = str(an), mink
%o A367813         while k in aset or Ld(s, str(k)) != 3: k += 1
%o A367813         an = k
%o A367813         aset.add(k)
%o A367813         while mink in aset: mink += 1
%o A367813 print(list(islice(agen(), 72))) # _Michael S. Branicky_, Dec 01 2023
%Y A367813 Cf. A118763, A367812, A367814, A367815.
%K A367813 base,nonn
%O A367813 1,2
%A A367813 _Eric Angelini_ and _Giorgos Kalogeropoulos_, Dec 01 2023