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 .
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 
.
