Odious number
In number theory, an odious number is a positive integer that has an odd number of 1s in its binary expansion.
The first odious numbers are:
These numbers give the positions of the nonzero values in the Thue–Morse sequence.
Non-negative integers that are not odious are called evil numbers. The partition of the non-negative integers into the odious and evil numbers is the unique partition of these numbers into two sets that have equal multisets of pairwise sums.
If denotes the th odious number, then for all,.
In computer science, an odious number is said to have odd parity.
