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.

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, 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, 9, 2, 1, 9, 3, 2, 2, 9, 5, 2, 5, 10, 11, 4

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Mar 15 2010

Keywords

• easy
• nonn
• base
• less

Comments

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.

Examples

			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~.
The pieces left are 10, 1, 0, 1, 10, 11, 0, ... which is in base 10: 2, 1, 0, 1, 2, 3, 0, ....
		

Crossrefs

Cf. A174204, A174205, A174206, A174207, A174208, A174209, A174210.

Programs

Maple

n1 := 1 ; n0 := 1 ;
for n from 0 to 80 do
        if n = 0 then b := [0] ; else b := convert(n,base,2) ; end if;
        for d from nops(b) to 1 by -1 do
                if op(d,b) = 0 then
                        if type(n0,'odd') then b := subsop(d=NULL,b) ; end if; n0 := n0+1 ;
                else
                        if type(n1,'odd') then b := subsop(d=NULL,b) ; end if; n1 := n1+1 ;
                end if;
        end do:
        add(2^(i-1)*op(i,b),i=1..nops(b)) ; printf("%d,",%) ;
end do: # R. J. Mathar, Nov 23 2010

Extensions

Sequence extended, keyword:base,less added by R. J. Mathar, Nov 23 2010