A235127 Greatest k such that 4^k divides n.

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

Crossrefs

Cf. A004526, A007814, A007949, A122841, A115362, A234957, A244413.

Sequence in context: A129251 A276077 A276935 * A358345 A258059 A093956

Adjacent sequences: A235124 A235125 A235126 * A235128 A235129 A235130

Keyword

nonn,easy

Author

Tom Edgar, Jan 03 2014

Extensions

More terms from Antti Karttunen, Nov 18 2017

Status

approved