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

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A118763, A367812, A367814, A367815.

Programs

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]

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