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