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A196564
Number of odd digits in decimal representation of n.
53
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
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
KEYWORD
nonn,easy,base
AUTHOR
Reinhard Zumkeller, Oct 04 2011
STATUS
approved