A174207 Depleted stream of the natural numbers written in base 2: delete even occurrences of digit 0 and odd occurrences of digit 1.

0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

Keywords

• easy
• nonn
• base

Comments

The numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000, ....

The infinite stream of digits: 0110111001011101111000...

Delete even (2nd, 4th, 6th, ...) occurrences of 0 (replaced by ~):

011~1110~10111~11110~0...

Delete odd (1st, 3rd, 5th, ...) occurrences of 1 (replaced by ~):

0~1~~1~0~10~1~~1~1~0~0...

Digits remaining define the sequence: 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, ....

Crossrefs

Cf. A174203, A174204 (base 10), A174205, A174206, A174208-A174210.

Programs

Maple

nb := 100 ;
L := [0] ;
for n from 1 to nb do
    nn := ListTools[Reverse](convert(n,base,2)) ;
    L := [op(L),op(nn)] ;
end do;
Lout := [] ;
ie :=1 ;
io :=1 ;
for i from 1 to nops(L) do
    if op(i,L) =0 then
        if ie>0 then
            if type(ie,'odd') then
                printf("%d,",0) ;
            end if;
        end if;
        ie := ie+1 ;
    else
        if io>0 then
            if type(io,'even') then
                printf("%d,",1) ;
            end if;
        end if;
        io := io+1 ;
    end if;
end do: # R. J. Mathar, Dec 06 2011

Mathematica

nMax = 60; bits = Join @@ Table[IntegerDigits[n, 2], {n, 0, nMax}]; pos0 = Position[bits, 0] // Flatten; even0 = Partition[pos0, 2][[All, 2]]; bits2 = ReplacePart[bits, Alternatives @@ even0 -> "~"]; pos1 = Position[bits2, 1] // Flatten; odd1 = Partition[pos1, 2][[All, 1]]; DeleteCases[ ReplacePart[ bits2, Alternatives @@ odd1 -> "~"], "~"] (* Jean-François Alcover, Nov 18 2016 *)