Abstract
For a set A, let P(A) be the set of all finite subset sums of A. We prove that if a sequence B={b 1<b 2<⋯} of integers satisfies b 1≧11 and b n+1≧3b n +5 (n=1,2,…), then there exists a sequence of positive integers A={a 1<a 2<⋯} for which P(A)=ℕ∖B. On the other hand, if a sequence B={b 1<b 2<⋯} of positive integers satisfies either b 1=10 or b 2=3b 1+4, then there is no sequence A of positive integers for which P(A)=ℕ∖B.
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References
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This work was supported by the National Natural Science Foundation of China, Grant No. 11071121.
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Chen, YG., Fang, JH. On a problem in additive number theory. Acta Math Hung 134, 416–430 (2012). https://doi.org/10.1007/s10474-011-0157-4
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DOI: https://doi.org/10.1007/s10474-011-0157-4