Odd Number
An Integer of the form 
, where 
is an Integer. The odd numbers are therefore ..., 
,
, 1, 3, 5, 7, ... (Sloane's A005408), which are also the Gnomic Numbers. TheGenerating Function for the odd numbers is
Since the odd numbers leave a remainder of 1 when divided by two, 
for odd 
. Integers which are notodd are called Even.
References
Sloane, N. J. A. SequenceA005408/M2400in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
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