A367812 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 2.

0, 11, 2, 10, 3, 12, 4, 13, 5, 14, 6, 15, 7, 16, 8, 17, 9, 18, 20, 1, 22, 19, 21, 30, 23, 31, 24, 32, 25, 33, 26, 34, 27, 35, 28, 36, 29, 37, 40, 38, 41, 39, 42, 50, 43, 51, 44, 52, 45, 53, 46, 54, 47, 55, 48, 56, 49, 57, 60, 58, 61, 59, 62, 70, 63, 71, 64, 72, 65, 73, 66, 74, 67, 75, 68, 76, 69, 77, 80, 78

Offset

1,2

Links

Table of n, a(n) for n=1..80.

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

Example

a(1) =  0 and a(2) = 11 are separated by an Ld of 2
a(2) = 11 and a(3) =  2 are separated by an Ld of 2
a(3) =  2 and a(4) = 10 are separated by an Ld of 2
a(4) = 10 and a(5) =  3 are separated by an Ld of 2, 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]!=2, k++]; k); Array[a, 80]

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)) != 2: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 80))) # Michael S. Branicky, Dec 01 2023

Crossrefs

Cf. A118763, A367813, A367814, A367815.

Sequence in context: A107831 A064928 A074335 * A284212 A273877 A066795

Adjacent sequences: A367809 A367810 A367811 * A367813 A367814 A367815

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Status

approved