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.

0, 111, 2, 100, 3, 101, 4, 102, 5, 103, 6, 104, 7, 105, 8, 106, 9, 107, 21, 108, 22, 109, 23, 110, 24, 112, 20, 113, 25, 114, 26, 115, 27, 116, 28, 117, 29, 118, 30, 119, 32, 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

Offset

1,2

Links

Table of n, a(n) for n=1..72.

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

Example

a(1) =   0 and a(2) = 111 are separated by a Ld of 3
a(2) = 111 and a(3) =   2 are separated by a Ld of 3
a(3) =   2 and a(4) = 100 are separated by a Ld of 3
a(4) = 100 and a(5) =   3 are separated by a Ld of 3, 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]!=3, k++]; k); Array[a, 72]

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)) != 3: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 72))) # Michael S. Branicky, Dec 01 2023

Crossrefs

Cf. A118763, A367812, A367814, A367815.

Sequence in context: A123698 A123727 A282915 * A351059 A279800 A282360

Adjacent sequences: A367810 A367811 A367812 * A367814 A367815 A367816

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Status

approved