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URL: https://oeis.org/A139353

⇱ A139353 - OEIS

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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).
10
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
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
(Fortran) c See link in A139351
KEYWORD
nonn,base
AUTHOR
STATUS
approved