A367797 The successive digits of the number k are the successive "inside Levenshtein distances" of k (except for the last digit of k). See the Comment section for the definition of an "inside Levenshtein distance".

10, 12, 13, 14, 15, 16, 17, 18, 19, 111, 211, 2020, 2122, 2230, 2231, 2234, 2235, 2236, 2237, 2238, 2239, 3121, 31131, 32131, 32233, 32340, 32341, 32345, 32346, 32347, 32348, 32349, 42232, 422242, 432242, 432450, 432451, 432456, 432457, 432458, 432459, 433242, 433344, 532342, 5433353, 5433455, 5433560

Offset: 1

Author

Eric Angelini and Giorgos Kalogeropoulos, Nov 30 2023

Keywords

• base
• nonn

Comments

Let's consider 2023 and compute the successive traditional Levenshtein distances between 2 and 023, 20 and 23, 202 and 3 (the so-called inside Lds).

We have:

Ld 2<>023 = 2,

Ld 20<>23 = 1,

Ld 202<>3 = 3.

The successive Lds of 2023 are 2, 1 and 3.

Examples

			a(1) = 10 has an iLd of 1 (the Levenshtein distance between 1 and 0) and this iLd of 1 is the first digit of a(1);
a(47) = 5433560 is in the sequence because its successive Lds are:
  Ld 5<>433560 = 5
  Ld 54<>33560 = 4
  Ld 543<>3560 = 3
  Ld 5433<>560 = 3
  Ld 54335<>60 = 5
  Ld 543356<>0 = 6.
We see that the rightmost column above reproduces a(47), except for the last digit.
		

Links

• Éric Angelini, Inside Levenshtein distances, Personal blog, November 2023.

Crossrefs

Cf. A367638.

Programs

Python

from Levenshtein import distance as Ld
def ok(n):
    s = str(n)
    if n < 10: return False # convention, though condition is vacuously True
    return all(Ld(s[:i+1], s[i+1:]) == int(s[i]) for i in range(len(s)-1))
print([k for k in range(10**7) if ok(k)]) # Michael S. Branicky, Dec 01 2023