On the sumset of the primes and a linear recurrence
Volume 161 / 2013
Acta Arithmetica 161 (2013), 33-46 MSC: 11P32, 11B37. DOI: 10.4064/aa161-1-3
Romanoff (1934) showed that integers that are the sum of a prime and a power of $2$ have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.