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A196564 Number of odd digits in decimal representation of n.

%I A196564 #52 Feb 16 2025 01:02:16
%S A196564 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,
%T A196564 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,
%U A196564 0,1,1,2,1,2,1,2,1,2,1,2,0,1,0,1,0,1
%N A196564 Number of odd digits in decimal representation of n.
%H A196564 Reinhard Zumkeller, <a href="/A196564/b196564.txt">Table of n, a(n) for n = 0..10000</a>
%H A196564 Zachary P. Bradshaw and Christophe Vignat, <a href="https://arxiv.org/abs/2307.05565">Dubious Identities: A Visit to the Borwein Zoo</a>, arXiv:2307.05565 [math.HO], 2023.
%F A196564 a(n) = A055642(n) - A196563(n);
%F A196564 a(A014263(n)) = 0; a(A007957(n)) > 0.
%F A196564 From _Hieronymus Fischer_, May 30 2012: (Start)
%F A196564 a(n) = Sum_{j=0..m} (floor(n/(2*10^j) + (1/2)) - floor(n/(2*10^j))), where m=floor(log_10(n)).
%F A196564 a(10*n+k) = a(n) + a(k), 0<=k<10, n>=0.
%F A196564 a(n) = a(floor(n/10)) + a(n mod 10), n>=0.
%F A196564 a(n) = Sum_{j=0..m} a(floor(n/10^j) mod 10), n>=0.
%F A196564 a(A014261(n)) = floor(log_5(4*n+1)), n>0.
%F A196564 G.f.: g(x) = (1/(1-x))*Sum_{j>=0} x^10^j/(1+x^10^j). (End)
%p A196564 A196564 := proc(n)
%p A196564         if n =0 then
%p A196564                 0;
%p A196564         else
%p A196564                 convert(n,base,10) ;
%p A196564                 add(d mod 2,d=%) ;
%p A196564         end if:
%p A196564 end proc: # _R. J. Mathar_, Jul 13 2012
%t A196564 Table[Total[Mod[IntegerDigits[n],2]],{n,0,100}] (* _Zak Seidov_, Oct 13 2015 *)
%o A196564 (Haskell)
%o A196564 a196564 n = length [d | d <- show n, d `elem` "13579"]
%o A196564 -- _Reinhard Zumkeller_, Feb 22 2012, Oct 04 2011
%o A196564 (PARI) a(n) = #select(x->x%2, digits(n)); \\ _Michel Marcus_, Oct 14 2015
%o A196564 (Python)
%o A196564 def a(n): return sum(1 for d in str(n) if d in "13579")
%o A196564 print([a(n) for n in range(100)]) # _Michael S. Branicky_, May 15 2022
%Y A196564 Cf. A014261, A014263, A027868, A046034, A055640, A055641, A055642, A061217, A102669-A102685, A122640, A196563.
%K A196564 nonn,easy,base
%O A196564 0,12
%A A196564 _Reinhard Zumkeller_, Oct 04 2011