A292597 a(1) = 1; for n > 1, a(n) = c(n) + 2*a(floor(n/2)), where c(n) is the characteristic function of odd composites, A071904.

1, 2, 2, 4, 4, 4, 4, 8, 9, 8, 8, 8, 8, 8, 9, 16, 16, 18, 18, 16, 17, 16, 16, 16, 17, 16, 17, 16, 16, 18, 18, 32, 33, 32, 33, 36, 36, 36, 37, 32, 32, 34, 34, 32, 33, 32, 32, 32, 33, 34, 35, 32, 32, 34, 35, 32, 33, 32, 32, 36, 36, 36, 37, 64, 65, 66, 66, 64, 65, 66, 66, 72, 72, 72, 73, 72, 73, 74, 74, 64, 65, 64, 64, 68, 69, 68, 69, 64, 64, 66, 67

Offset: 1

Author

Antti Karttunen, Sep 27 2017

Keywords

• nonn

Comments

1-bits in base-2 expansion of a(n) indicate the positions of odd nonprimes in the sequence [n, floor(n/2), floor(n/4), ..., 1].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000035, A010051, A014076, A071904, A292596, A292598.

Formula

a(1) = 1; for n > 1, a(n) = (A000035(n)*(1-A010051(n))) + 2*a(floor(n/2)).

For all n >= 1, a(n) + A292596(n) = n.