Abstract
Let 0 ≦ a 1 < a 2 < ⋯ be an infinite sequence of integers and let r 1(A, n) = |(i;j): a i + a j = n, i ≦ j|. We show that if d > 0 is an integer, then there does not exist n 0 such that d ≦ r 1 (A, n) ≦ d + [√2d + ½] for n > n 0.
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References
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Horváth, G. On additive representation function of general sequences. Acta Math Hung 115, 169–175 (2007). https://doi.org/10.1007/s10474-007-5230-7
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DOI: https://doi.org/10.1007/s10474-007-5230-7