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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 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 *) 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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