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Odd Number

An Integer of the form $N=2n+1$, where $n$ is an Integer. The odd numbers are therefore ..., $-3$, $-1$, 1, 3, 5, 7, ... (Sloane's A005408), which are also the Gnomic Numbers. The Generating Function for the odd numbers is


Since the odd numbers leave a remainder of 1 when divided by two, $N\equiv 1\ \left({{\rm mod\ } {2}}\right)$ for odd $N$. Integers which are not odd are called Even.

See also Even Number, Gnomic Number, Nicomachus's Theorem, Odd Number Theorem, Odd Prime


Sloane, N. J. A. Sequence A005408/M2400 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein