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On the sumset of the primes and a linear recurrence

Volume 161 / 2013

Christian Ballot, Florian Luca 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.


  • Christian BallotL.M.N.O., CNRS UMR 6139
    Université de Caen
    F-14032 Caen Cedex, France
  • Florian LucaFundación Marcos Moshinsky
    Circuito Exterior, C.U., Apdo. Postal 70-543
    México, D.F. 04510, México

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