[seqfan] Champernowne sieved

[Eric Angelini]

Hello SeqFans,
consider http://oeis.org/A033307
(decimal expansion of Champernowne's constant):
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 4, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 5, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5,...

Now erase a digit when it is placed 
between two digits having the same parity -- and
do this repeatedly. 

Example:
1,2,3,... erase 2
You get now:
1,3,4,5,... erase 4
You get now:
1,3,5,... erase 3
You get now:
1,5,6,7,... erase 6
You get now:
1,5,7,... erase 5 etc.

Two seq might be of interest;
1) R, the surviving digits: 
R=1,9,2,2,9,9,4,4,9,9,6,6,9,9,8,8,9,1,0,0,1,1,0,2,1,1,0,4,1,1,0,6,1,1,0,8,1,1,2,0,1,1,2,2,3,1,2,2,1,9,2,2,9,9,4,4,9,9,6,6,9,9,8,8,9,1,0,0,1,1,0,2,1,1,0,4,1,1,0,6,1,1,0,8,1,1,2,0,1,2,2,3,1,2,2,5,1,2,2,7,1,2,2,9,1,4,0,1,4,4,3,1,4,4,5,1,4,4,7,1,4,4,9,1,6,0,1,1,6,2,1,...

2) U, the original "untouched" natural integers:
U=1,29,49,69,89,102,104,106,108,120,140,160,162,...

(R and U computed by hand... don't
trust those figures too much)
Best,
É.