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Number of even digits in decimal representation of n.
53

%I #38 Jul 25 2023 10:59:10

%S 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,2,1,2,1,2,1,2,1,2,1,1,0,1,0,

%T 1,0,1,0,1,0,2,1,2,1,2,1,2,1,2,1,1,0,1,0,1,0,1,0,1,0,2,1,2,1,2,1,2,1,

%U 2,1,1,0,1,0,1,0,1,0,1,0,2,1,2,1,2,1

%N Number of even digits in decimal representation of n.

%H Reinhard Zumkeller, <a href="/A196563/b196563.txt">Table of n, a(n) for n = 0..10000</a>

%H 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 a(n) = A055642(n) - A196564(n);

%F a(A014261(n)) = 0; a(A007928(n)) > 0.

%F From _Hieronymus Fischer_, May 30 2012: (Start)

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

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

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

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

%F a(A014263(n)) = 1 + floor(log_5(n-1)), n>1.

%F G.f.: g(x) = 1 + (1/(1-x))*sum_{j>=0} x^(2*10^j)/(1+ x^10^j). (End)

%p A196563 := proc(n)

%p if n =0 then

%p 1;

%p else

%p convert(n,base,10) ;

%p add(1-(d mod 2),d=%) ;

%p end if:

%p end proc: # _R. J. Mathar_, Jul 13 2012

%t Table[Count[Mod[IntegerDigits[n],2],0][n],{n,0,100}] (* _Zak Seidov_, Oct 13 2015 *)

%t Table[Count[IntegerDigits[n],_?EvenQ],{n,0,120}] (* _Harvey P. Dale_, Feb 22 2020 *)

%o (Haskell)

%o a196563 n = length [d | d <- show n, d `elem` "02468"]

%o -- _Reinhard Zumkeller_, Feb 22 2012, Oct 04 2011

%o (PARI) a(n) = #select(x->(!(x%2)), if (n, digits(n), [0])); \\ _Michel Marcus_, Oct 14 2015

%o (Python)

%o def a(n): return sum(1 for d in str(n) if d in "02468")

%o print([a(n) for n in range(100)]) # _Michael S. Branicky_, May 15 2022

%Y Cf. A014261, A014263, A027868, A046034, A055640, A055641, A055642, A061217, A102669-A102685, A122640, A196564.

%K nonn,base

%O 0,21

%A _Reinhard Zumkeller_, Oct 04 2011