On the sumset of the primes and a linear recurrence

Christian Ballot, and Florian Luca. "On the sumset of the primes and a linear recurrence." Acta Arithmetica 161.1 (2013): 33-46. <http://eudml.org/doc/286068>.

@article{ChristianBallot2013,
abstract = {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.},
author = {Christian Ballot, Florian Luca},
journal = {Acta Arithmetica},
keywords = {Goldbach-type theorems; linear recurrence; primes; sumsets; asymptotic density; S-units},
language = {eng},
number = {1},
pages = {33-46},
title = {On the sumset of the primes and a linear recurrence},
url = {http://eudml.org/doc/286068},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Christian Ballot
AU - Florian Luca
TI - On the sumset of the primes and a linear recurrence
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 1
SP - 33
EP - 46
AB - 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.
LA - eng
KW - Goldbach-type theorems; linear recurrence; primes; sumsets; asymptotic density; S-units
UR - http://eudml.org/doc/286068
ER -