Definition:Proth Number

Definition
A Proth number is a natural number of the form:
 * $N = k \times 2^n + 1$

where:
 * $k$ is an odd integer
 * $n$ is a positive integer
 * $2^n > k$

The condition is included, otherwise every odd integer greater than $1$ would be a Proth number.

Also see

 * Definition:Proth Prime
 * Proth's Theorem