A352784 a(n) = w(n - w(n)), where w(n) is the binary weight of n, A000120(n).

0, 0, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 3, 3, 4, 4, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 5, 5, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 5, 5, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 4, 4, 6, 6, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 5, 5, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 4, 4, 5, 5, 6, 6, 3, 3, 3, 3, 4, 4, 4, 4

Offset: 0

Author

Ctibor O. Zizka, Apr 02 2022

Keywords

• nonn
• base
• easy

Examples

			a(8) = A000120(8 - A000120(8)) = 3.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000120, A011371, A280700.

Programs

Maple

a:= n-> (w-> w(n-w(n)))(k-> add(i, i=Bits[Split](k))):
seq(a(n), n=0..120);  # Alois P. Heinz, May 24 2022

Mathematica

w[n_] := DigitCount[n, 2, 1]; a[n_] := w[n - w[n]]; Array[a, 100, 0] (* Amiram Eldar, Apr 02 2022 *)

Python

def w(n): return bin(n).count("1")
def a(n): return w(n - w(n))
print([a(n) for n in range(108)]) # Michael S. Branicky, Apr 02 2022

Formula

a(n) = A000120(n - A000120(n)); a(n) = A000120(A011371(n)).

a(n) = A280700(floor(n/2)). - Georg Fischer, Nov 29 2022