Odious number

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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:

1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38 ... [1]

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.

In computer science, an odious number is said to have odd parity.


  1. ^ Sloane, N. J. A. (ed.). "Sequence A000069 (Odious numbers: numbers with an odd number of 1's in their binary expansion)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

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