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

23, 27, 29, 30, 639, 703, 735, 751, 759, 763, 765, 766, 831, 863, 879, 887, 891, 893, 894, 927, 943, 951, 955, 957, 958, 975, 983, 987, 989, 990, 999, 1003, 1005, 1006, 1011, 1013, 1014, 1017, 1018, 1020, 18431, 19455, 19967, 20223, 20351, 20415

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Keywords

• nonn
• base

Comments

The ratio of 1's over 0's is 4:1. Subset of A143909.

Examples

			The 29 is in the sequence because it reads A007088(29)= 11101 in base 2, and 4 of the 5 digits are 1.
The 1003 is in the sequence because it reads A007088(1003)= 1111101011 in base 2, and 8 of the 10 digits are 1.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..2551

Crossrefs

Cf. A031443, A137254, A163140, A000120, A023416, A143909, A007088.

Programs

Mathematica

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
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 *)
d80Q[n_]:=Module[{idn2=DigitCount[n,2]},idn2[[1]]==4*idn2[[2]]]; Select[ Range[25000],d80Q] (* Harvey P. Dale, Mar 18 2012 *)

Formula

{n: A000120(n)=4*A023416(n) }.

Extensions

Edited by R. J. Mathar, Jul 25 2009