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A174207 Depleted stream of the natural numbers written in base 2: delete even occurrences of digit 0 and odd occurrences of digit 1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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,....

LINKS

Table of n, a(n) for n=0..118.

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-Fran├žois Alcover, Nov 18 2016 *)

CROSSREFS

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

Sequence in context: A073070 A099104 A066829 * A048820 A144101 A127000

Adjacent sequences:  A174204 A174205 A174206 * A174208 A174209 A174210

KEYWORD

easy,nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

STATUS

approved

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Last modified December 7 05:39 EST 2016. Contains 278841 sequences.