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 A234957 #45 Dec 31 2022 03:44:19
%S A234957 1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,16,1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,16,1,
%T A234957 1,1,4,1,1,1,4,1,1,1,4,1,1,1,16,1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,64,1,1,
%U A234957 1,4,1,1,1,4,1,1,1,4,1,1,1,16
%N A234957 Highest power of 4 dividing n.
%C A234957 The generalized binomial coefficients produced by this sequence provide an analog to Kummer's Theorem using arithmetic in base 4.
%C A234957 In the binary representation of n, remove zeros from the right until the number of zeros is even, then remove all but the rightmost one bit. - _Ralf Stephan_, Jan 05 2014
%H A234957 G. C. Greubel, <a href="/A234957/b234957.txt">Table of n, a(n) for n = 1..1000</a>
%H A234957 Tyler Ball, Tom Edgar, and Daniel Juda, <a href="http://dx.doi.org/10.4169/math.mag.87.2.135">Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem</a>, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
%H A234957 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%F A234957 a(n) = 4^(valuation(n,4)).
%F A234957 a(n) = 4^(floor(valuation(n,2)/2)) = 4^A004526(A007814(n)). Recurrence: a(4n) = 4a(n), a(4n+k) = 1 for k=1,2,3. - _Ralf Stephan_, Jan 05 2014
%F A234957 G.f.: x/(1 - x) + 3 * Sum_{k>=1} 4^(k-1)*x^(4^k)/(1 - x^(4^k)). - _Ilya Gutkovskiy_, Jul 10 2019
%F A234957 From _Amiram Eldar_, Dec 31 2022: (Start)
%F A234957 Multiplicative with a(2^e) = 2^(2*floor(e/2)), and a(p^e) = 1 if p >= 3.
%F A234957 Dirichlet g.f.: zeta(s)*(4^s-1)/(4^s-4).
%F A234957 Sum_{k=1..n} a(k) ~ (3/(8*log(2)))*n*log(n) + (5/8 + 3*(gamma-1)/(8*log(2)))*n, where gamma is Euler's constant (A001620). (End)
%e A234957 Since 8=4*2, then a(8)=4. Likewise, since 4 does not divide 9, a(9)=1.
%t A234957 Table[4^(IntegerExponent[n, 4]), {n, 1, 50}] (* _G. C. Greubel_, Apr 13 2017 *)
%o A234957 (Sage)
%o A234957 n=200 #change n for more terms
%o A234957 [4^(valuation(i,4)) for i in [1..n]]
%o A234957 (PARI) a(n)=4^valuation(n,4) \\ _Charles R Greathouse IV_, Aug 05 2015
%o A234957 (Python)
%o A234957 def A234957(n): return 1<<((~n&n-1).bit_length()&-2) # _Chai Wah Wu_, Jul 08 2022
%Y A234957 Cf. A001620, A006519, A038500.
%K A234957 nonn,easy,mult
%O A234957 1,4
%A A234957 _Tom Edgar_, Jan 01 2014
%E A234957 Keyword:mult added by _Andrew Howroyd_, Jul 23 2018