Proth number

A Proth number $p$ is a number of the form $k{2}^m+1$, where $k$ is odd (e.g., $k=2n+1$ with an integer $n>(-1)$), $m$ is also an integer and $2^m>k$. The first few Proth numbers are 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, etc. (listed in A080075 of Sloane’s OEIS). The Fermat numbers are a subset of the Proth numbers, namely with $k=1$.