A367810 Lexicographically earliest sequence of distinct positive terms not ending in 0 such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to the last digit of a(n).

1, 2, 11, 12, 3, 101, 102, 13, 201, 21, 22, 4, 1001, 1002, 103, 5, 10001, 10002, 1003, 14, 2001, 2002, 203, 6, 100001, 100002, 10003, 104, 2211, 211, 111, 112, 15, 20001, 20002, 202, 23, 105, 22211, 2221, 221, 121, 122, 16, 200001, 200002, 20003, 204, 1111, 1011, 1012, 106, 222211, 22221, 2222, 212, 17

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Keywords

• base
• nonn

Examples

			a(1) =  1 and a(2) =   2 are separated by an Ld of 1, and 1 is the last digit of a(1)
a(2) =  2 and a(3) =  11 are separated by an Ld of 2, and 2 is the last digit of a(2)
a(3) = 11 and a(4) =  12 are separated by an Ld of 1, and 1 is the last digit of a(3)
a(4) = 12 and a(5) =   3 are separated by an Ld of 2, and 2 is the last digit of a(4)
a(5) =  3 and a(6) = 101 are separated by an Ld of 3, and 3 is the last digit of a(5), etc.
		

Links

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

Crossrefs

Cf. A367638.

Programs

Mathematica

a[1]=1;a[n_]:=a[n]=(k=1; While[MemberQ[Array[a,n-1],k] ||Mod[k,10]==0|| EditDistance[ToString@a[n-1],ToString@k]!= Mod[a[n-1],10],k++];k);Array[a,40]

Python

from itertools import islice
from Levenshtein import distance as Ld
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 2
    while True:
        yield an
        s, k = str(an), mink
        target = int(s[-1])
        while k%10 == 0 or k in aset or Ld(s, str(k)) != target: k += 1
        an = k
        aset.add(k)
        while mink in aset or mink%10 == 0: mink += 1
print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 01 2023