Definition:Thabit Number
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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 $\mathsf{Pr} \infty \mathsf{fWiki}$.
Also see
- Results about Thabit numbers can be found here.
Source of Name
This entry was named for Thabit ibn Qurra.
Sources
- Weisstein, Eric W. "Thâbit ibn Kurrah Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThabitibnKurrahNumber.html