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

Author

Pontus von Brömssen, Dec 26 2018

Keywords

• nonn
• base

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).

Examples

			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.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 0..1000
• Wikipedia, Damerau-Levenshtein distance

Crossrefs

Cf. A152487, A322285, A099627, A079071.