Abstract
Let h, k be fixed positive integers, and let A be any set of positive integers. Let hA ≔ {a 1 + a 2 + ... + a r : a i ∈ A, r ⩽ h} denote the set of all integers representable as a sum of no more than h elements of A, and let n(h, A) denote the largest integer n such that {1, 2,...,n} ⊆ hA. Let n(h, k) := \( \mathop {\max }\limits_A \): n(h, A), where the maximum is taken over all sets A with k elements. We determine n(h, A) when the elements of A are in geometric progression. In particular, this results in the evaluation of n(h, 2) and yields surprisingly sharp lower bounds for n(h, k), particularly for k = 3.
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Tripathi, A. The postage stamp problem and arithmetic in base r . Czech Math J 58, 1097–1100 (2008). https://doi.org/10.1007/s10587-008-0071-2
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DOI: https://doi.org/10.1007/s10587-008-0071-2