A139353 Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k's that are even, o(n) the number that are odd; sequence gives e(n)*o(n).

0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 2, 1, 2, 2, 4, 0, 0, 1, 2, 0, 0, 2, 3, 1, 2, 2, 4, 2, 3, 4, 6, 0, 1, 0, 2, 1, 2, 2, 4, 0, 2, 0, 3, 2, 4, 3, 6, 1, 2, 2, 4, 2, 3, 4, 6, 2, 4, 3, 6, 4, 6, 6, 9, 0, 0, 1, 2, 0, 0, 2, 3, 1, 2, 2, 4, 2, 3, 4, 6, 0, 0, 2, 3, 0, 0, 3, 4, 2, 3, 4, 6, 3, 4, 6, 8, 1, 2, 2

Offset

0,8

Comments

e(n) + o(n) = A000120(n), the binary weight of n.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n) = A139351(n) * A139352(n). - Amiram Eldar, Jul 18 2023

Example

If n = 43 = 2^0+2^2+2^3+2^5, e(43)=1, o(43)=3.

Mathematica

e[0] = 0; e[n_] := e[n] = e[Floor[n/4]] + If[OddQ[Mod[n, 4]], 1, 0];
o[0] = 0; o[n_] := o[n] = o[Floor[n/4]] + If[Mod[n, 4] > 1, 1, 0];
a[n_] := e[n] * o[n]; Array[a, 100, 0] (* Amiram Eldar, Jul 18 2023 *)

Prog

See link in A139351 for Fortran program.

Crossrefs

Cf. A000120, A139351, A139352, A139354, A139355, A039004, A139370, A139371, A139372, A139373.

Sequence in context: A259965 A117054 A036579 * A345219 A357705 A363945

Adjacent sequences: A139350 A139351 A139352 * A139354 A139355 A139356

Keyword

nonn,base

Author

Nadia Heninger and N. J. A. Sloane, Jun 07 2008

Status

approved