Cullen number

This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers

Definition

Suppose $n$ is a natural number. The Cullen number parametrized by $n$, denoted $C_{n}$, is defined as:

$C_{n}:=n\cdot 2^{n}+1$

Relation with other properties

Weaker properties

• Proth number: A Proth number is a number of the form $k\cdot 2^{n}+1$, $k<2^{n}$. Since $n<2^{n}$ for all $n$, any Cullen number is a Proth number.

Other related properties

• Fermat number is a number of the form $2^{2^{n}}+1$, and is also a special case of a Proth number.
• Sierpinski number is a number of the form $k\cdot 2^{n}-1$, with $k<2^{n}$.