Geodesic
On the sumset of the primes and a linear recurrence
Christian Ballot 1   ; Florian Luca 2
1 L.M.N.O., CNRS UMR 6139 Université de Caen F-14032 Caen Cedex, France
2 Fundación Marcos Moshinsky UNAM Circuito Exterior, C.U., Apdo. Postal 70-543 México, D.F. 04510, México
Acta Arithmetica, Tome 161 (2013) no. 1, pp. 33-46 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa161-1-3
Keywords: romanoff showed integers sum prime nbsp power have positive lower asymptotic density positive integers adapt his method showing generally existence positive lower asymptotic density integers sum prime nbsp term nbsp given nonconstant nondegenerate integral linear recurrence separable characteristic polynomial

Christian Ballot  1   ; Florian Luca  2

1 L.M.N.O., CNRS UMR 6139 Université de Caen F-14032 Caen Cedex, France
2 Fundación Marcos Moshinsky UNAM Circuito Exterior, C.U., Apdo. Postal 70-543 México, D.F. 04510, México 
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Christian Ballot; Florian Luca. On the sumset of the primes and a linear recurrence. Acta Arithmetica, Tome 161 (2013) no. 1, pp. 33-46. doi: 10.4064/aa161-1-3

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