A317922 a(n) = number of k with 0 < 2*k < n-1 such that a(n-k) AND a(n-2*k) = a(n-k) (where AND denotes the bitwise AND operator).

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

Offset: 1

Author

Rémy Sigrist, Aug 11 2018

Keywords

• nonn
• base

Comments

This sequence has similarities with A317420.

Examples

			For n = 5:
- a(5-1) AND a(5-2) = 0 AND 1 = 0 = a(5-1),
- a(5-2) AND a(5-4) = 1 AND 0 = 0 <> a(5-2),
- hence a(5) = 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..50000
• Rémy Sigrist, Scatterplot of the first 10000000 terms
• Rémy Sigrist, Colored scatterplot of the first 10000000 terms (where the color is function of the 2-adic valuation of n (A001511))
• Rémy Sigrist, Colored scatterplot of the first 10000000 terms (where the color is function of A000265(n) mod 16)
• Rémy Sigrist, C++ program for A317922

Crossrefs

Cf. A000265, A001511, A317420.