A078839 - OEIS

%I #24 Apr 28 2024 16:29:37

%S 2,12,69,73,150,184,252,328,339,464,483,541,729,747,758,763,1014,1047,

%T 1090,1094,1158,1264,1359,1601,1679,1693,1698,1780,2368,2641,2815,

%U 3292,3393,3606,3682,3857,3909,3919,3963,4087,4111,4289,4314,5017,5398,5466

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

%C Does the limit of a(n)/n^2 as n -> infinity exist?

%H Hugo Pfoertner, <a href="/A078839/b078839.txt">Table of n, a(n) for n = 1..1600</a> (terms 1..1000 from Amiram Eldar)

%H Amiram Eldar, <a href="/A078839/a078839.jpg">Plot of a(n)/n^2 for n = 1..1000</a>

%H 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 balanced[n_] := Module[{d=IntegerDigits[n, 2]}, Plus@@d==Length[d]/2]; Select[Range[0, 5500], balanced[3^# ]&]

%o (PARI) is(n)=hammingweight(n=3^n)==hammingweight(bitneg(n,#binary(n))) \\ _Charles R Greathouse IV_, Mar 29 2013

%Y Cf. A000244, A004656, A011754, A031443.

%K nonn,base

%O 1,1

%A _Benoit Cloitre_, Dec 06 2002