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Parity

The parity of a number $n$ 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.

$N$ Binary Parity $N$ 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.




© 1996-9 Eric W. Weisstein
1999-05-26