This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A235127 #31 Jul 26 2024 09:14:13
%S A235127 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 A235127 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 A235127 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 A235127 Greatest k such that 4^k divides n.
%H A235127 Antti Karttunen, <a href="/A235127/b235127.txt">Table of n, a(n) for n = 1..65537</a>
%F A235127 a(n) = valuation(n,4).
%F A235127 G.f.: Sum_{k>=1} x^(4^k)/(1 - x^(4^k)). - _Ilya Gutkovskiy_, Jan 28 2017
%F A235127 a(n) = A004526(A007814(n)). - _Antti Karttunen_, Nov 18 2017
%F A235127 Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/3. - _Amiram Eldar_, Jan 17 2022
%e A235127 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 A235127 IntegerExponent[Range@ 105, 4] (* _Michael De Vlieger_, Nov 18 2017 *)
%o A235127 (PARI) A235127(n) = valuation(n,4); \\ _Antti Karttunen_, Nov 18 2017
%o A235127 (Sage)
%o A235127 n=100 #change n for more terms
%o A235127 [valuation(i,4) for i in [1..n]]
%o A235127 (Python)
%o A235127 def A235127(n): return (~n&n-1).bit_length()>>1 # _Chai Wah Wu_, Jul 08 2022
%Y A235127 Cf. A004526, A007814, A007949, A122841, A115362, A234957, A244413.
%K A235127 nonn,easy
%O A235127 1,16
%A A235127 _Tom Edgar_, Jan 03 2014
%E A235127 More terms from _Antti Karttunen_, Nov 18 2017