I think the form you are looking for is 2^nk. You can do a Google search for "Dual Sierpinski problem" to find more details.
NewPGen supports the sieving of b^n+/k with fixed k.
As for sieving multiple k's one after the other, I think you should be able to use the "Sieve Until..." Option. Here you can set stop criteria for how far to sieve a single k, and the increment the k and move on.
You might also want to look at PFGW for such things, since you'll also be able to test the candidates for primality.
