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A163142 Integers n such that exactly 80 percent of the digits in base 2 are 1's.

%I A163142 #13 Oct 12 2015 14:17:10
%S A163142 23,27,29,30,639,703,735,751,759,763,765,766,831,863,879,887,891,893,
%T A163142 894,927,943,951,955,957,958,975,983,987,989,990,999,1003,1005,1006,
%U A163142 1011,1013,1014,1017,1018,1020,18431,19455,19967,20223,20351,20415
%N A163142 Integers n such that exactly 80 percent of the digits in base 2 are 1's.
%C A163142 The ratio of 1's over 0's is 4:1. Subset of A143909.
%H A163142 Zak Seidov, <a href="/A163142/b163142.txt">Table of n, a(n) for n = 1..2551</a>
%F A163142 {n: A000120(n)=4*A023416(n) }.
%e A163142 The 29 is in the sequence because it reads A007088(29)= 11101 in base 2, and 4 of the 5 digits are 1.
%e A163142 The 1003 is in the sequence because it reads A007088(1003)= 1111101011 in base 2, and 8 of the 10 digits are 1.
%t A163142 f0[n_]:=DigitCount[n,2,0]; f1[n_]:=DigitCount[n,2,1]; f[n_]:=f1[n]/f0[n]; lst={};Do[If[f[n]==3,AppendTo[lst,n]],{n,8!}];lst
%t A163142 ZS={};Do[dc=DigitCount[n,2];If[dc[[1]]==4*dc[[2]],AppendTo[ZS,n]],{n,10,10^6}];ZS (* _Zak Seidov_, Jul 28 2009 *)
%t A163142 d80Q[n_]:=Module[{idn2=DigitCount[n,2]},idn2[[1]]==4*idn2[[2]]]; Select[ Range[25000],d80Q] (* _Harvey P. Dale_, Mar 18 2012 *)
%Y A163142 Cf. A031443, A137254, A163140, A000120, A023416, A143909, A007088.
%K A163142 nonn,base
%O A163142 1,1
%A A163142 _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009
%E A163142 Edited by _R. J. Mathar_, Jul 25 2009