A Proth number is a number of the form 
for odd k, n a positive integer, and 
. 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, ... (Sloane's A080075).
The Cullen numbers are a special case of the Proth numbers with k = n (and the inequality restriction dropped). The Fermat numbers are a special case of the Proth numbers with k = 1.
Cullen Number, Cunningham Number, Proth Prime, Sierpinski's Composite Number Theorem, Sierpinski Number of the Second Kind
McNamara, J. and Mills, M. "Factoring of Proth Numbers." http://www.fidn.org/proth1.html.
Sloane, N. J. A. Sequences A080075 in "The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/.