A175879 Numbers arising from certain regular binary expansions.

0, 1, 2, 7, 12, 29, 58, 123, 240, 501, 998, 2023, 4040, 8137, 16266, 32671, 65300, 130837, 261682, 523827, 1047592, 2096237, 4192366, 8386671, 16773312, 33550545, 67100882, 134210007, 268419484, 536854941, 1073709994, 2147451819

Offset

0,3

Comments

Consider infinite 0-1 matrix (which expands left and down).

Last column is 010101 ... (alters every step)

Previous is 00110011 ... (alters every 2 steps)

Previous to previous is 000111000111 ... (alters every 3 steps)

Etc. ...

Now a(n) are values of binary numbers coded by rows.

Links

Table of n, a(n) for n=0..31.

Formula

a(0) = 0;

a(n) = \sum_{k=1}^n 2^{k-1}\odd(n \div k)

Maple

Contribution from R. J. Mathar, Oct 08 2010: (Start)
A175879 := proc(n) local a, k, ndivk ; a := 0 ; for k from 1 to n do ndivk := floor(n/k) ; if type(ndivk, 'odd') then a := a+2^(k-1) ; fi ; end do: a ; end proc:
seq(A175879(n), n=0..40) ; (End)

Mathematica

 f[n_] := Sum[ If[ OddQ[ Floor[ n/k]], 2^(k - 1), 0], {k, n}]; Array[f, 32, 0]

Prog

(Pascal pseudocode)
var n, a, p, k : integer;
readln(n); (* read index *)
p:= 1; (* powers of 2 *)
a:= 0;
for k:= 1 to n do
begin
if odd( n div k ) then a:= a+p;
p:= 2*p
end;
writeln(a); (* here a = a(n) *)
(* Kamburelis Anastasios (akamb(AT)epp.teicrete.gr), Oct 09 2010 *)

Crossrefs

Sequence in context: A177747 A288888 A293621 * A102371 A007230 A290234

Adjacent sequences: A175876 A175877 A175878 * A175880 A175881 A175882

Keyword

easy,nonn

Author

Kamburelis Anastasios (akamb(AT)epp.teicrete.gr), Oct 07 2010

Extensions

Extended by R. J. Mathar, Oct 08 2010

Status

approved