# Definition:Woodall Number

## 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.

## Source of Name

This entry was named for Herbert J. Woodall.