A367814 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 4.

0, 1111, 2, 1000, 3, 1001, 4, 1002, 5, 1003, 6, 1004, 7, 1005, 8, 1006, 9, 1007, 21, 1008, 22, 1009, 23, 1010, 24, 1011, 25, 1012, 26, 1013, 27, 1014, 28, 1015, 29, 1016, 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

Offset

1,2

Links

Table of n, a(n) for n=1..64.

Éric Angelini, More Levenshtein distances, Personal blog, December 2023.

Example

a(1) =    0 and a(2) = 1111 are separated by an Ld of 4
a(2) = 1111 and a(3) =    2 are separated by an Ld of 4
a(3) =    2 and a(4) = 1000 are separated by an Ld of 4
a(4) = 1000 and a(5) =    3 are separated by an Ld of 4, etc.

Mathematica

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]

Prog

(Python)
from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 0, {0}, 1
    while True:
        yield an
        s, k = str(an), mink
        while k in aset or Ld(s, str(k)) != 4: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 64))) # Michael S. Branicky, Dec 01 2023

Crossrefs

Cf. A118763, A367812, A367813, A367815.

Sequence in context: A147589 A287283 A277927 * A086887 A278870 A278898

Adjacent sequences: A367811 A367812 A367813 * A367815 A367816 A367817

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Status

approved