OFFSET
0,21
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.
FORMULA
From Hieronymus Fischer, May 30 2012: (Start)
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)
MAPLE
A196563 := proc(n)
if n =0 then
1;
else
convert(n, base, 10) ;
add(1-(d mod 2), d=%) ;
end if:
end proc: # R. J. Mathar, Jul 13 2012
MATHEMATICA
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 *)
PROG
(Haskell)
a196563 n = length [d | d <- show n, d `elem` "02468"]
-- Reinhard Zumkeller, Feb 22 2012, Oct 04 2011
(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")
print([a(n) for n in range(100)]) # Michael S. Branicky, May 15 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Oct 04 2011
STATUS
approved