A Proth number is a number of the form for odd ,
a positive integer, and .
The condition is needed since otherwise,
every odd number
would be a Proth number. The first few Proth numbers are 3, 5, 9, 13, 17, 25, 33,
41, 49, 57, 65, ... (OEIS A080075).

The Cullen numbers are a special case of the Proth numbers with
(and the inequality restriction dropped). The Fermat
numbers are a special case of the Proth numbers with .

McNamara, J. and Mills, M. "Factoring of Proth Numbers." http://www.fidn.org/proth1.html.Sloane,
N. J. A. Sequence A080075 in "The
On-Line Encyclopedia of Integer Sequences."