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A174203 In the sequence A007088 of binary representations of n, delete the 1st, 3rd, 5th, 7th, 9th etc occurrence of 0 and 1. Rewrite the bits left over in base 10.

%I A174203 #12 May 11 2019 11:41:43
%S A174203 2,1,0,1,2,3,0,2,2,5,2,1,6,3,0,2,4,5,2,1,5,3,2,2,5,5,2,3,6,7,0,4,4,9,
%T A174203 2,1,10,3,4,2,10,5,2,5,5,11,4,2,10,5,2,5,5,11,2,6,6,13,6,3,14,7,0,4,8,
%U A174203 9,2,1,9,3,2,2,9,5,2,5,10,11,4
%N A174203 In the sequence A007088 of binary representations of n, delete the 1st, 3rd, 5th, 7th, 9th etc occurrence of 0 and 1. Rewrite the bits left over in base 10.
%C A174203 Deleting the odd occurrences of 0 and the even occurrences of 1, we get the same sequence apart from the initial 2 replaced by 1 and 0.
%e A174203 Numbers in base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000, .... Delete odd occurrences of 0 (replaced by ~): ~, 1, 10, 11, 1~0, 1~1, 110, 111, 1~0~ Delete odd occurrences of 1 (replaced by ~): ~, ~, 10, ~1, ~~0, 1~~, 1~0, 1~1, ~~0~.
%e A174203 The pieces left are 10, 1, 0, 1, 10, 11, 0, ... which is in base 10: 2, 1, 0, 1, 2, 3, 0, ....
%p A174203 n1 := 1 ; n0 := 1 ;
%p A174203 for n from 0 to 80 do
%p A174203         if n = 0 then b := [0] ; else b := convert(n,base,2) ; end if;
%p A174203         for d from nops(b) to 1 by -1 do
%p A174203                 if op(d,b) = 0 then
%p A174203                         if type(n0,'odd') then b := subsop(d=NULL,b) ; end if; n0 := n0+1 ;
%p A174203                 else
%p A174203                         if type(n1,'odd') then b := subsop(d=NULL,b) ; end if; n1 := n1+1 ;
%p A174203                 end if;
%p A174203         end do:
%p A174203         add(2^(i-1)*op(i,b),i=1..nops(b)) ; printf("%d,",%) ;
%p A174203 end do: # _R. J. Mathar_, Nov 23 2010
%Y A174203 Cf. A174204, A174205, A174206, A174207, A174208, A174209, A174210.
%K A174203 easy,nonn,base,less
%O A174203 0,1
%A A174203 _Paolo P. Lava_ and _Giorgio Balzarotti_, Mar 15 2010
%E A174203 Sequence extended, keyword:base,less added by _R. J. Mathar_, Nov 23 2010