A322795 Number of integers k, 0 <= k <= n, such that the Damerau-Levenshtein distance between the binary representations of n and k is strictly less than the Levenshtein distance.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 1, 0, 2, 1, 3, 0, 4, 4, 4, 1, 4, 2, 4, 0, 0, 0, 1, 0, 2, 1, 3, 0, 4, 5, 5, 1, 5, 4, 7, 0, 8, 9, 9, 6, 8, 8, 8, 1, 8, 8, 8, 2, 8, 4, 8, 0, 0, 0, 1, 0, 2, 1, 4, 0, 4, 6, 6, 1, 5, 4, 9, 0, 8, 11, 11, 7, 10, 11, 11, 1, 10, 12, 13, 5, 13, 9, 14, 0, 16, 18, 17, 15, 16

Offset

0,13

Comments

a(n) = 0 if and only if n appears in A099627 or n = 0.

a(n) = A079071(n) for n <= 21, but a(22) = 3 > 2 = A079071(22).

Links

Pontus von Brömssen, Table of n, a(n) for n = 0..1000

Wikipedia, Damerau-Levenshtein distance

Example

For n = 6, the Damerau-Levenshtein distance and the Levenshtein distance between the binary representations of n and k are equal for all k <= n except k = 5. The Levenshtein distance between 101 and 110 (5 and 6 in binary) is 2, whereas the Damerau-Levenshtein distance is 1, so a(6) = 1.

Crossrefs

Cf. A152487, A322285, A099627, A079071.

Sequence in context: A175620 A319812 A079071 * A050602 A065040 A284688

Adjacent sequences: A322792 A322793 A322794 * A322796 A322797 A322798

Keyword

nonn,base

Author

Pontus von Brömssen, Dec 26 2018

Status

approved