A137254 -id:A137254 - cp's OEIS frontend

A163140 Integers n such that in base 2, 3 `1`'s for each `0`.

11, 13, 14, 159, 175, 183, 187, 189, 190, 207, 215, 219, 221, 222, 231, 235, 237, 238, 243, 245, 246, 249, 250, 252, 2303, 2431, 2495, 2527, 2543, 2551, 2555, 2557, 2558, 2687, 2751, 2783, 2799, 2807, 2811, 2813, 2814, 2879, 2911, 2927, 2935, 2939, 2941

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

There are (4n-1 choose n) 4n-bit members of this sequence for each n=1,2,.... - Charles R Greathouse IV, Oct 12 2009

			IntegerDigits[11,2]={1,0,1,1},..IntegerDigits[190,2]={1,0,1,1,1,1,1,0},..

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A031443, A137254, A000120

sort([seq(op(map(proc(t) local j; 2^(4*n)-1-add(2^(j-1),j=t) end proc, combinat:-choose(4*n-1,n))),n=1..3)]);

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,7!}];lst
Select[Range[3000],DigitCount[#,2,1]==3*DigitCount[#,2,0]&] (* Harvey P. Dale, May 31 2015 *)

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

Original entry on oeis.org

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

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

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

			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.

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

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

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 *)

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

Edited by R. J. Mathar, Jul 25 2009

cp's OEIS Frontend

A163140 Integers n such that in base 2, 3 `1`'s for each `0`.

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