A228584 Start with decimal expansion of Champernowne constant (A033307) and repeatedly remove the first digit between two neighbors (after the decimal point) having the same parity.

1, 9, 2, 2, 9, 9, 4, 4, 9, 9, 6, 6, 9, 9, 8, 8, 9, 1, 0, 0, 1, 1, 0, 0, 3, 1, 0, 0, 5, 1, 0, 0, 7, 1, 0, 0, 9, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 5, 1, 2, 2, 7, 1, 2, 2, 9, 1, 4, 4, 1, 1, 4, 4, 3, 1, 4, 4, 5, 1, 4, 4, 7, 1, 4, 4, 9, 1, 6, 6, 1, 1, 6, 6, 3, 1, 6, 6, 5, 1, 6, 6, 7, 1, 6, 6, 9, 1, 8, 8, 1, 1, 8, 8, 3

Offset: 0

Author

Alois P. Heinz, Aug 26 2013

Keywords

• nonn
• cons
• base

Comments

Parity of digits is 1, 1, 0, 0, ... = A133872.

Examples

			Start with 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.
The surviving digits are this sequence:
1,9,2,2,9,9,4,4,9,9,6,6,9,9,8,8,9,1,0,0,1,1,0,...
and the original "untouched" positive integers, A228585:
1, 29, 49, 69, 89, 219, 239, 259, 279, 419, 439, ...
We obtain a new constant,
0.1922994499669988910011003100510071...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Eric Angelini et al., Champernowne sieved and follow-up messages on the SeqFan list, Aug 26 2013

Crossrefs

Cf. A033307, A133872, A228585 (untouched numbers in the removal process).