Evil number
In number theory, an evil number is a non-negative integer that has an even number of 1s in its binary expansion. These numbers give the positions of the zero values in the Thue–Morse sequence, and for this reason they have also been called the Thue–Morse set. Non-negative integers that are not evil are called odious numbers. Examples. The first evil numbers are: Equal sums. 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 . As 19th-century mathematician Eugène Prouhet showed, the partition into evil and odious numbers of the numbers from formula_1 to formula_2, for any formula_3, provides a solution to the Prouhet–Tarry–Escott problem of finding sets of numbers whose sums of powers are equal up to the formula_3th power. In computer science. In computer science, an evil number is said to have even parity.