A135585 a(n) = Sum_{i=1..n} (floor(S2(i)/3) mod 2), where S2(i) = A000120(i).

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 16, 16, 16, 17, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 41, 41, 41, 41, 42

Offset: 0

Author

Ctibor O. Zizka, Feb 25 2008

Keywords

• easy
• nonn
• base

Comments

Sequence A115384 is a(n) = Sum_{i=1..n} (floor(S2(n)*1/1) mod 2) = Sum_{i=1..n} (S2(n) mod 2).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A115384, A010060.

Programs

Maple

A000120 := proc(n) local i ; add(i,i=convert(n,base,2)) : end: A135585 := proc(n) add(floor(A000120(i)/3) mod 2,i=1..n) ; end: seq(A135585(n),n=0..80) ; # R. J. Mathar, Apr 22 2008

Mathematica

f[n_] := n - Sum[Floor[n/2^k], {k, 1, Infinity}]; Table[Sum[Mod[Floor[f[i]/3], 2], {i,1,n}], {n,0,25}] (* G. C. Greubel, Oct 20 2016 *)

PARI

a(n) = sum(i=1, n, hammingweight(i)\3 % 2); \\ Michel Marcus, Sep 19 2015

Extensions

Definition corrected by R. J. Mathar, Apr 22 2008