On integers which are the sum of a power of 2 and a polynomial value

@inproceedings{Luca2013OnIW,
  title={On integers which are the sum of a power of 2 and a polynomial value},
  author={Florian Luca and Carlos Gustavo Moreira and Carl Pomerance},
  year={2013}
}
Here, we show that if f(x) ∈ Z[x] has degree at least 2 then the set of integers which are of the form 2k+f(m) for some integers k ≥ 0 and m is of asymptotic density 0. We also make some conjectures and prove some results about integers not of the form |2k ±ma(m− 1)|.