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 A386260 #9 Jul 18 2025 08:30:50
%S A386260 1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,
%T A386260 1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,3,1,1,1,2,
%U A386260 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1
%N A386260 Maximum exponent in the prime factorization of the exponent of the highest power of 2 dividing 2*n.
%C A386260 The first occurrence of k = 1, 2, ... is at n = 2^(2^k-2) = A051191(k).
%C A386260 The asymptotic density of the occurrences of 1 in this sequence is 4 * Sum_{k squarefree > 1} (1/2^k - 1/2^(k+1)) = 0.862752712766... .
%H A386260 Amiram Eldar, <a href="/A386260/b386260.txt">Table of n, a(n) for n = 1..10000</a>
%F A386260 a(n) = A051903(A001511(2*n)).
%F A386260 A051903(A001511(2*n-1)) = 0 for all n >= 1, and therefore the odd-indexed terms of A051903(A001511(n)) are omitted.
%F A386260 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=2} A051903(k)/2^(k-1) = 1.14512095789925078232... . If the odd-indexed zero terms had not been omitted, the asymptotic mean would be half this value, 0.57256047894962539116... .
%t A386260 a[n_] := Module[{v = IntegerExponent[n, 2] + 2}, If[v == 1, 0, Max[FactorInteger[v][[;;, 2]]]]]; Array[a, 100]
%o A386260 (PARI) a(n) = my(v = valuation(4*n, 2)); if(v == 1, 0, vecmax(factor(v)[,2]));
%Y A386260 Cf. A001511, A051191, A051903.
%K A386260 nonn,easy
%O A386260 1,4
%A A386260 _Amiram Eldar_, Jul 17 2025