A317420 a(n) = number of k with 1 <= k <= n-1 such that a(k) AND a(n-k) = a(k) (where AND denotes the bitwise AND operator).

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

Offset: 1

Author

Rémy Sigrist, Jul 27 2018

Keywords

• nonn
• base

Comments

This sequence was inspired by A055224.

See also A317419, A317441, A317443 and A317585 for similar sequences; these sequences can be defined as a(n) = Sum_{k=1..n-1} [P(a(k), a(n-k))] for some predicate P in two variables (where [] is an Iverson bracket).

Examples

			For n = 4:
- a(1) AND a(3) = 0 AND 1 = 0 = a(1),
- a(2) AND a(2) = 1 AND 1 = 1 = a(2),
- a(3) AND a(1) = 1 AND 0 = 0 <> a(3),
- hence a(4) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055224, A317419, A317441, A317443, A317585.

Programs

PARI

a = vector(75); for (n=1, #a, a[n] = sum(k=1, n-1, bitand(a[k], a[n-k])==a[k]); print1 (a[n] ", "))