# Definition:Woodall Number

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## Definition

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

- $n \times 2^n - 1$

### Sequence

The sequence of **Woodall numbers** begins:

- $1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, \ldots$

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

## Also known as

Some sources refer to numbers of the form $n \times 2^n - 1$ as **Cullen numbers**, along with those of the form $n \times 2^n + 1$.

However, it is now conventional to reserve the term **Cullen numbers**, named for James Cullen, to those of the form $n \times 2^n + 1$.

The latter are also known as **Cunningham numbers**, for Allan Joseph Champneys Cunningham, so as to ensure their unambiguous distinction from **Woodall numbers**.

## Also see

## Source of Name

This entry was named for Herbert J. Woodall.

## Sources

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