A235127 - OEIS

%I #31 Jul 26 2024 09:14:13

%S 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,

%T 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,

%U 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

%N Greatest k such that 4^k divides n.

%H Antti Karttunen, <a href="/A235127/b235127.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = valuation(n,4).

%F G.f.: Sum_{k>=1} x^(4^k)/(1 - x^(4^k)). - _Ilya Gutkovskiy_, Jan 28 2017

%F a(n) = A004526(A007814(n)). - _Antti Karttunen_, Nov 18 2017

%F Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/3. - _Amiram Eldar_, Jan 17 2022

%e 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.

%t IntegerExponent[Range@ 105, 4] (* _Michael De Vlieger_, Nov 18 2017 *)

%o (PARI) A235127(n) = valuation(n,4); \\ _Antti Karttunen_, Nov 18 2017

%o (Sage)

%o n=100 #change n for more terms

%o [valuation(i,4) for i in [1..n]]

%o (Python)

%o def A235127(n): return (~n&n-1).bit_length()>>1 # _Chai Wah Wu_, Jul 08 2022

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

%K nonn,easy

%O 1,16

%A _Tom Edgar_, Jan 03 2014

%E More terms from _Antti Karttunen_, Nov 18 2017