On the integers not of the form $p+2^a+2^b$

TL;DR

This paper demonstrates that the set of odd integers not expressible as the sum of a prime and two powers of two has a density that is significantly large, growing faster than any power of x less than 1.

Contribution

It establishes a lower bound on the size of the set of odd integers not of the form p+2^a+2^b, showing it is very large in a quantitative sense.

Findings

The set of odd integers not of the form p+2^a+2^b has size at least proportional to x^{1- ext{epsilon}}.

The result holds for any epsilon > 0, with the implied constant depending only on epsilon.

This indicates the abundance of integers that cannot be expressed in the given form.

Abstract

We prove that |{1<=y<=x: y is odd and not of the form p+2^a+2^b}|>>x^{1-\epsilon} for any \epsilon>0, where the implied constant only depends on \epsilon.