A171823 a(n) = base-2 concatenation XYZ, where X = number of bits in binary expansion of n, Y = number of 0's, Z = number of 1's.

101, 1011, 10010, 11101, 11110, 11110, 11011, 100111, 1001010, 1001010, 100111, 1001010, 100111, 100111, 1000100, 1011001, 1011110, 1011110, 1011011, 1011110, 1011011, 1011011, 1011100, 1011110, 1011011, 1011011, 1011100, 1011011, 1011100, 1011100

Offset: 1

Author

N. J. A. Sloane, Oct 16 2010

Keywords

• nonn
• base

Examples

			14 = 1110 in base 2, so X = 4 = 100, Y = 1, Z = 3 = 11, a(14) = 100.1.11 = 100111.
		

Crossrefs

Cf. A171825, A171798, A171813.

Programs

Maple

F:=proc(n) local t1,t2,t2b,n1,n1b,n0,n0b,t3,t4;
t1:=convert(n,base,2);
t2:=nops(t1);
t2b:=convert(t2,base,2);
n1:=add(t1[i],i=1..t2);
n1b:=convert(n1,base,2);
n0:=t2-n1;
n0b:=convert(n0,base,2);
t3:=[
seq(t2b[nops(t2b)+1-i],i=1..nops(t2b)),
seq(n0b[nops(n0b)+1-i],i=1..nops(n0b)),
seq(n1b[nops(n1b)+1-i],i=1..nops(n1b))
];
t4:="";
for i from 1 to nops(t3) do t4:=cat(t4,t3[i]); od:
parse(t4);
end;

Mathematica

a[n_] := IntegerDigits[{z, y} = DigitCount[n, 2]; {y+z, y, z}, 2] // Flatten // FromDigits; Array[a, 30] (* Jean-François Alcover, Oct 20 2016 *)