Romanoff theorem in a sparse set |
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Authors: | Yong-Gao Chen |
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Affiliation: | 1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, China
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Abstract: | Let A be any subset of positive integers, and P the set of all positive primes. Two of our results are: (a) the number of positive integers which are less than x and can be represented as 2 k + p (resp. p ? 2 k ) with k ∈ A and p ∈ P is more than 0.03A(log x/ log 2)π(x) for all sufficiently large x; (b) the number of positive integers which are less than x and can be represented as 2 q + p with p, q ∈ P is (1 + o(1)π(log x/ log 2)π(x). Four related open problems and one conjecture are posed. |
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