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A367797
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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".
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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PROG
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(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))
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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