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A196563
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Number of even digits in decimal representation of n.
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53
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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, 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, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1
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OFFSET
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0,21
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LINKS
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FORMULA
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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)).
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(A014263(n)) = 1 + floor(log_5(n-1)), n>1.
G.f.: g(x) = 1 + (1/(1-x))*sum_{j>=0} x^(2*10^j)/(1+ x^10^j). (End)
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MAPLE
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if n =0 then
1;
else
convert(n, base, 10) ;
add(1-(d mod 2), d=%) ;
end if:
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MATHEMATICA
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Table[Count[Mod[IntegerDigits[n], 2], 0][n], {n, 0, 100}] (* Zak Seidov, Oct 13 2015 *)
Table[Count[IntegerDigits[n], _?EvenQ], {n, 0, 120}] (* Harvey P. Dale, Feb 22 2020 *)
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PROG
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(Haskell)
a196563 n = length [d | d <- show n, d `elem` "02468"]
(PARI) a(n) = #select(x->(!(x%2)), if (n, digits(n), [0])); \\ Michel Marcus, Oct 14 2015
(Python)
def a(n): return sum(1 for d in str(n) if d in "02468")
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CROSSREFS
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Cf. A014261, A014263, A027868, A046034, A055640, A055641, A055642, A061217, A102669-A102685, A122640, A196564.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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