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

1,2

Links

Table of n, a(n) for n=1..57.

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

Example

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.

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]

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)) != 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

Crossrefs

Cf. A118763, A367812, A367813, A367814.

Sequence in context: A235405 A360034 A158619 * A094324 A347911 A346001

Adjacent sequences: A367812 A367813 A367814 * A367816 A367817 A367818

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Dec 01 2023

Status

approved