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 
.
