A367815 Lexicographically earliest sequence of distinct nonnegative terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to 5.

0, 11111, 2, 10000, 3, 10001, 4, 10002, 5, 10003, 6, 10004, 7, 10005, 8, 10006, 9, 10007, 21, 10008, 22, 10009, 23, 10010, 24, 10011, 25, 10012, 26, 10013, 27, 10014, 28, 10015, 29, 10016, 32, 10017, 33, 10018, 34, 10019, 35, 10020, 31, 10022, 36, 10021, 37, 10023, 38, 10024, 39, 10025, 41, 10026, 43

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Keywords

• base
• nonn

Examples

			a(1) =     0 and a(2) = 11111 are separated by an Ld of 5
a(2) = 11111 and a(3) = 1   2 are separated by an Ld of 5
a(3) =     2 and a(4) = 10000 are separated by an Ld of 5
a(4) = 10000 and a(5) =     3 are separated by an Ld of 5, etc.
		

Links

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

Crossrefs

Cf. A118763, A367812, A367813, A367814.

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]!=5,k++];k);Array[a,57]

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)) != 5: k += 1
        an = k
        aset.add(k)
        while mink in aset: mink += 1
print(list(islice(agen(), 57))) # Michael S. Branicky, Dec 01 2023