Proth prime

In number theory, a Proth number, named after the mathematician François Proth, is a number of the form

where ${\displaystyle k}$ is an odd positive integer and ${\displaystyle n}$ is a positive integer such that ${\displaystyle 2^{n}>k}$. Without the latter condition, all odd integers greater than 1 would be Proth numbers.

The first few Proth numbers are (sequence in the OEIS):

The Cullen numbers (n·2ⁿ+1) and Fermat numbers (2²ⁿ+1) are special cases of Proth numbers.

...
Wikipedia