Definition:Cullen Number

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

• Definition:Cullen Prime

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