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

0,2

Comments

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

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

Example

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...

Crossrefs

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

Sequence in context: A200298 A110543 A319026 * A021056 A132719 A293577

Adjacent sequences: A228581 A228582 A228583 * A228585 A228586 A228587

Keyword

nonn,cons,base

Author

Alois P. Heinz, Aug 26 2013

Status

approved