Riesel number

In mathematics, a Riesel number is an odd natural number k for which ${\displaystyle k\times 2^{n}-1}$ is composite for all natural numbers n (sequence A101036 in the OEIS). In other words, when k is a Riesel number, all members of the following set are composite:

${\displaystyle \left\{\,k\times 2^{n}-1:n\in \mathbb {N} \,\right\}.}$

If the form is instead ${\displaystyle k\times 2^{n}+1}$, then k is a Sierpiński number.