A367814 - OEIS

%I #13 Dec 21 2023 15:18:50

%S 0,1111,2,1000,3,1001,4,1002,5,1003,6,1004,7,1005,8,1006,9,1007,21,

%T 1008,22,1009,23,1010,24,1011,25,1012,26,1013,27,1014,28,1015,29,1016,

%U 32,1017,33,1018,34,1019,35,1020,31,1022,36,1021,37,1023,38,1024,39,1025,41,1026,43,1027,44,1028,45,1029,46,1030

%N Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 4.

%H Éric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/12/more-levenshtein-distances.html">More Levenshtein distances</a>, Personal blog, December 2023.

%e a(1) =    0 and a(2) = 1111 are separated by an Ld of 4

%e a(2) = 1111 and a(3) =    2 are separated by an Ld of 4

%e a(3) =    2 and a(4) = 1000 are separated by an Ld of 4

%e a(4) = 1000 and a(5) =    3 are separated by an Ld of 4, etc.

%t a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=4,k++];k);Array[a,64]

%o (Python)

%o from itertools import islice

%o from Levenshtein import distance as Ld

%o def agen(): # generator of terms

%o     an, aset, mink = 0, {0}, 1

%o     while True:

%o         yield an

%o         s, k = str(an), mink

%o         while k in aset or Ld(s, str(k)) != 4: k += 1

%o         an = k

%o         aset.add(k)

%o         while mink in aset: mink += 1

%o print(list(islice(agen(), 64))) # _Michael S. Branicky_, Dec 01 2023

%Y Cf. A118763, A367812, A367813, A367815.

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Dec 01 2023