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 A383032 #13 Apr 13 2025 14:56:16
%S A383032 0,1,2,3,0,4,1,0,5,2,0,1,6,3,0,1,2,0,7,4,1,0,2,3,0,1,8,5,0,2,1,0,3,4,
%T A383032 0,1,2,9,0,6,1,0,3,2,1,0,4,5,0,1,2,0,3,10,1,0,7,2,0,1,4,3,0,2,1,0,5,6,
%U A383032 0,1,2,3,0,1,4,0,11,2,1,0,8,3,0,1,2,5,0
%N A383032 Exponent of the highest power of 2 dividing the n-th number that is either a square or twice a square.
%C A383032 The first position of k in this sequence, for k >= 0, is A001521(k+1).
%H A383032 Amiram Eldar, <a href="/A383032/b383032.txt">Table of n, a(n) for n = 1..10000</a>
%F A383032 a(n) = A007814(A028982(n)).
%F A383032 a(A001954(n)) = 0 for n >= 0.
%F A383032 a(A215247(n)) = 1 for n >= 1.
%F A383032 a(A342280(n)) = 2 for n >= 0.
%F A383032 Sum_{k=1..n} a(k) ~ (1 + sqrt(2)) * n.
%t A383032 With[{m = 3000}, IntegerExponent[Union[Join[Range[Floor[Sqrt[m]]]^2, 2*Range[Floor[Sqrt[m/2]]]^2]], 2]]
%o A383032 (PARI) lista(nn) = apply(x->valuation(x,2), vecsort(concat(vector(sqrtint(nn\1), i, i^2), vector(sqrtint(nn\2), i, 2*i^2)))); \\ _Michel Marcus_, Apr 13 2025
%Y A383032 Cf. A001521, A001954, A003151, A003152, A007814, A014176, A028982, A215247, A342280.
%K A383032 nonn,easy
%O A383032 1,3
%A A383032 _Amiram Eldar_, Apr 13 2025