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