%I #14 May 12 2019 02:18:02

%S 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,

%T 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,

%U 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

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

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

%C The infinite stream of digits: 0110111001011101111000...

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

%C 011~1110~10111~11110~0...

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

%C 0~1~~1~0~10~1~~1~1~0~0...

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

%p nb := 100 ;

%p L := [0] ;

%p for n from 1 to nb do

%p nn := ListTools[Reverse](convert(n,base,2)) ;

%p L := [op(L),op(nn)] ;

%p end do;

%p Lout := [] ;

%p ie :=1 ;

%p io :=1 ;

%p for i from 1 to nops(L) do

%p if op(i,L) =0 then

%p if ie>0 then

%p if type(ie,'odd') then

%p printf("%d,",0) ;

%p end if;

%p end if;

%p ie := ie+1 ;

%p else

%p if io>0 then

%p if type(io,'even') then

%p printf("%d,",1) ;

%p end if;

%p end if;

%p io := io+1 ;

%p end if;

%p end do: # _R. J. Mathar_, Dec 06 2011

%t 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 *)

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

%K easy,nonn,base

%O 0,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Mar 15 2010