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, 4294902560, 8589870885, 17179739942

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..34.

Formula

a(n) = Sum_{k=1..n, floor(n/k) odd} 2^(k-1).

Maple

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) ; # R. J. Mathar, Oct 08 2010
# Alternative:
a:= n-> add(`if`(iquo(n, k)::odd, 2^(k-1), 0), k=1..n):
seq(a(n), n=0..34);  # Alois P. Heinz, Mar 21 2026

Mathematica

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

Prog

(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