Definition:Sierpiński Number of the Second Kind

Definition
A Sierpiński number of the second kind is an odd positive integer $k$ such that integers of the form $k2^n + 1$ are composite for all positive integers $n$.

That is, when $k$ is a Sierpiński number of the second kind, all members of the set:
 * $\left\{{k 2^n + 1}\right\}$

are composite.

Also known as
A Sierpiński number of the second kind is also often generally known as a Sierpiński number, as the Sierpiński numbers of the first kind have not received the same amount of attention.

However, since the philosophy of is to include all and everything, it is necessary to ensure full distinction is made between the two.

Hence, whenever used, the full title will be used for this entity throughout.

However, when discussing the nature of whether a given integer $n$ is a Sierpiński number of the second kind or not, it is commonplace, even on, to state: $n$ is / is not Sierpiński.

Also see

 * 78,557 is Sierpiński
 * Existence of Infinite Number of Numbers that are Riesel, Carmichael and Sierpiński


 * Definition:Riesel Number
 * Definition:Carmichael Number
 * Sierpiński Problem