A196564 Number of odd digits in decimal representation of n.

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 1

Offset

0,12

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Zachary P. Bradshaw and Christophe Vignat, Dubious Identities: A Visit to the Borwein Zoo, arXiv:2307.05565 [math.HO], 2023.

Formula

a(n) = A055642(n) - A196563(n);

a(A014263(n)) = 0; a(A007957(n)) > 0.

From Hieronymus Fischer, May 30 2012: (Start)

a(n) = Sum_{j=0..m} (floor(n/(2*10^j) + (1/2)) - floor(n/(2*10^j)), where m=floor(log_10(n)).

a(10n+k) = a(n) + a(k), 0<=k<10, n>=0.

a(n) = a(floor(n/10)) + a(n mod 10), n>=0.

a(n) = Sum_{j=0..m} a(floor(n/10^j) mod 10), n>=0.

a(A014261(n)) = floor(log_5(4n+1)), n>0.

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} x^10^j/(1+x^10^j).

(End)

Maple

A196564 := proc(n)
        if n =0 then
                0;
        else
                convert(n, base, 10) ;
                add(d mod 2, d=%) ;
        end if:
end proc: # R. J. Mathar, Jul 13 2012

Mathematica

Table[Total[Mod[IntegerDigits[n], 2]], {n, 0, 100}] (* Zak Seidov, Oct 13 2015 *)

Prog

(Haskell)
a196564 n = length [d | d <- show n, d `elem` "13579"]
-- Reinhard Zumkeller, Feb 22 2012, Oct 04 2011
(PARI) a(n) = #select(x->x%2, digits(n)); \\ Michel Marcus, Oct 14 2015
(Python)
def a(n): return sum(1 for d in str(n) if d in "13579")
print([a(n) for n in range(100)]) # Michael S. Branicky, May 15 2022

Crossrefs

Cf. A014261, A014263, A027868, A046034, A055640, A055641, A055642, A061217, A102669-A102685, A122640, A196563.

Sequence in context: A111621 A326398 A140195 * A196563 A198890 A305831

Adjacent sequences: A196561 A196562 A196563 * A196565 A196566 A196567

Keyword

nonn,easy,base

Author

Reinhard Zumkeller, Oct 04 2011

Status

approved