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

Author

Reinhard Zumkeller, Oct 04 2011

Keywords

• nonn
• easy
• base

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.

Crossrefs

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

Programs

Haskell

a196564 n = length [d | d <- show n, d `elem` "13579"]
-- Reinhard Zumkeller, Feb 22 2012, Oct 04 2011

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 *)

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

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(10*n+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(4*n+1)), n>0.

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