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A078839 Numbers k such that the binary expansion of 3^k has the same number of 0's and 1's.

%I A078839 #24 Apr 28 2024 16:29:37
%S A078839 2,12,69,73,150,184,252,328,339,464,483,541,729,747,758,763,1014,1047,
%T A078839 1090,1094,1158,1264,1359,1601,1679,1693,1698,1780,2368,2641,2815,
%U A078839 3292,3393,3606,3682,3857,3909,3919,3963,4087,4111,4289,4314,5017,5398,5466
%N A078839 Numbers k such that the binary expansion of 3^k has the same number of 0's and 1's.
%C A078839 Does the limit of a(n)/n^2 as n -> infinity exist?
%H A078839 Hugo Pfoertner, <a href="/A078839/b078839.txt">Table of n, a(n) for n = 1..1600</a> (terms 1..1000 from Amiram Eldar)
%H A078839 Amiram Eldar, <a href="/A078839/a078839.jpg">Plot of a(n)/n^2 for n = 1..1000</a>
%H A078839 Hugo Pfoertner, <a href="/plot2a?name1=A078839&amp;name2=A000290&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;drawpoints=true">Plot of a(n)/n^2</a> using Plot 2.
%t A078839 balanced[n_] := Module[{d=IntegerDigits[n, 2]}, Plus@@d==Length[d]/2]; Select[Range[0, 5500], balanced[3^# ]&]
%o A078839 (PARI) is(n)=hammingweight(n=3^n)==hammingweight(bitneg(n,#binary(n))) \\ _Charles R Greathouse IV_, Mar 29 2013
%Y A078839 Cf. A000244, A004656, A011754, A031443.
%K A078839 nonn,base
%O A078839 1,1
%A A078839 _Benoit Cloitre_, Dec 06 2002