An integer of the form $3 \cdot 2^n - 1$ or $2^{n + 1} + 2^n - 1$ They are listed in A055010 of Sloane's OEIS. The Thabit numbers are a subset of the Proth numbers.

The mathematician and astronomer Thabit ibn Qurra studied these numbers in search of a formula for amicable pairs. He found that when two consecutive Thabit numbers are also prime numbers (corresponding to indices $n$ and $n - 1$ and $9 \cdot 2^{2n - 1} - 1$ is a prime number, too, then these numbers multiplied by $2^n$ will reveal an amicable pair. The only $n$ known to fit these criteria are 2, 4 and 7. The largest Thabit number known to be prime corresponds to index 2312734, its immediate lower neighbor is composite.

It is conjectured that the nimfactorial of a Thabit number is always 2.