# Definition:Cullen Number

(Redirected from Definition:Cunningham Number)

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## Definition

A **Cullen number** is a positive integer of the form:

- $n \times 2^n + 1$

### Sequence

The sequence of **Cullen numbers** begins:

- $1, 3, 9, 25, 65, 161, 385, \ldots$

corresponding to $n = 0, 1, 2, 3, \ldots$

## Also defined as

Some sources refer to numbers of the form $n \times 2^n - 1$ as also being **Cullen numbers**.

However, it is now conventional to refer to numbers of the form $n \times 2^n - 1$ as **Woodall numbers**, for Herbert J. Woodall.

## Also known as

Some sources refer to **Cullen numbers** as **Cunningham numbers**, for Allan Joseph Champneys Cunningham, so as to ensure their distinction from **Woodall numbers**.

## Also see

## Source of Name

This entry was named for James Cullen.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $141$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $141$

- Weisstein, Eric W. "Cullen Number." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/CullenNumber.html