Sierpiński number

In number theory, a Sierpiński number is an odd natural number k such that ${\displaystyle k\times 2^{n}+1}$ is composite for all natural numbers n. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers k which have this property.

In other words, when k is a Sierpiński number, all members of the following set are composite:

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

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