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The parity of a number 
is the sum of the bits in Binary representation (mod 2). The parities of the first few
integers (starting with 0) are 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, ... (Sloane's A010060) summarized in the following table.
 |
Binary | Parity | |
Binary | Parity |
| 1 | 1 | 1 | 11 | 1011 | 1 |
| 2 | 10 | 1 | 12 | 1100 | 0 |
| 3 | 11 | 0 | 13 | 1101 | 1 |
| 4 | 100 | 1 | 14 | 1110 | 1 |
| 5 | 101 | 0 | 15 | 1111 | 0 |
| 6 | 110 | 0 | 16 | 10000 | 1 |
| 7 | 111 | 1 | 17 | 10001 | 0 |
| 8 | 1000 | 1 | 18 | 10010 | 0 |
| 9 | 1001 | 0 | 19 | 10011 | 1 |
| 10 | 1010 | 0 | 20 | 10100 | 0 |
The constant generated by the sequence of parity digits is called the Thue-Morse Constant.
See also Binary, Thue-Morse Constant
References
Sloane, N. J. A. Sequence
A010060
in ``The On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html.