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A235127
Greatest k such that 4^k divides n.
18
0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1
OFFSET
1,16
LINKS
FORMULA
a(n) = valuation(n,4).
G.f.: Sum_{k>=1} x^(4^k)/(1 - x^(4^k)). - Ilya Gutkovskiy, Jan 28 2017
a(n) = A004526(A007814(n)). - Antti Karttunen, Nov 18 2017
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/3. - Amiram Eldar, Jan 17 2022
EXAMPLE
Since 4^2 divides 32 and 4^3 does not, we have a(32) = 2. Likewise, since no positive power of 4 divides 9, a(9) = 0.
MATHEMATICA
IntegerExponent[Range@ 105, 4] (* Michael De Vlieger, Nov 18 2017 *)
PROG
(PARI) A235127(n) = valuation(n, 4); \\ Antti Karttunen, Nov 18 2017
(Sage)
n=100 #change n for more terms
[valuation(i, 4) for i in [1..n]]
(Python)
def A235127(n): return (~n&n-1).bit_length()>>1 # Chai Wah Wu, Jul 08 2022
KEYWORD
nonn,easy
AUTHOR
Tom Edgar, Jan 03 2014
EXTENSIONS
More terms from Antti Karttunen, Nov 18 2017
STATUS
approved