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

1,4

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).

Links

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

Example

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.

Prog

(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] ", "))

Crossrefs

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

Sequence in context: A241604 A282900 A126014 * A256795 A273404 A281976

Adjacent sequences: A317417 A317418 A317419 * A317421 A317422 A317423

Keyword

nonn,base

Author

Rémy Sigrist, Jul 27 2018

Status

approved