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.