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

0,5

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000120, A011371, A280700.

Sequence in context: A136480 A050603 A286554 * A037162 A352911 A278566

Adjacent sequences: A352781 A352782 A352783 * A352785 A352786 A352787

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Apr 02 2022

Status

approved