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 A383029 #8 Apr 13 2025 16:32:25
%S A383029 0,1,0,0,1,0,3,1,0,0,1,0,0,0,0,1,0,3,1,0,0,1,0,5,0,1,0,0,1,0,3,0,1,0,
%T A383029 1,0,0,0,1,0,3,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,3,0,0,0,1,0,
%U A383029 5,0,0,1,0,3,0,1,0,0,1,0,0,1,0,1,0,3,1
%N A383029 Exponent of the highest power of 2 dividing the n-th exponentially odd number.
%H A383029 Amiram Eldar, <a href="/A383029/b383029.txt">Table of n, a(n) for n = 1..10000</a>
%F A383029 a(n) = A007814(A268335(n)).
%F A383029 a(A383030(n)) > 0.
%F A383029 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2/3.
%t A383029 expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; IntegerExponent[Select[Range[200], expOddQ], 2]
%o A383029 (PARI) isexpodd(n) = {my(f = factor(n)); for(i=1, #f~, if(!(f[i, 2] % 2), return (0))); 1; }
%o A383029 list(lim) = for(k = 1, lim, if(isexpodd(k), print1(valuation(k, 2), ", ")));
%Y A383029 Cf. A007814, A268335, A383030.
%K A383029 nonn,easy
%O A383029 1,7
%A A383029 _Amiram Eldar_, Apr 13 2025