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

1,1

Links

Table of n, a(n) for n=1..30.

Example

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

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 *)

Crossrefs

Cf. A171825, A171798, A171813.

Sequence in context: A289578 A190619 A290197 * A289528 A289771 A131194

Adjacent sequences: A171820 A171821 A171822 * A171824 A171825 A171826

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 16 2010

Status

approved