# Definition:Thabit Number

## Definition

A Thabit number is an integer in the form:

$3 \times 2^n - 1$

where $n \in \Z_{\ge 0}$ is a non-negative integer.

### Sequence

The sequence of Thabit numbers begins:

$2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, \ldots$

## Also known as

A Thabit number is also known as a 321 number, from its form: $3$ times $2$ to the $n$th minus $1$.

Some sources give his name in full, or a rendition of it: Thâbit ibn Kurrah number.

The shorter form is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$.

## Source of Name

This entry was named for Thabit ibn Qurra.