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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.
3
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
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
KEYWORD
base,nonn
AUTHOR
STATUS
approved