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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Sums of distinct elements from a fixed set

Author: Torleiv Kløve
Journal: Math. Comp. 29 (1975), 1144-1149
MSC: Primary 10A40; Secondary 10B35
MathSciNet review: 0398969
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Abstract: A sequence of natural numbers is complete if every large integer is a sum of distinct elements of the sequence. The greatest integer which is not such a sum is called the threshold of completeness. Richert developed a method to compute the threshold of completeness. We prove that Richert’s method applies to a large class of complete sequences. Further, we consider in some detail these concepts for the sequences of powers (with fixed exponents) and give numerical results.

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Keywords: Sums of distinct integers, sums of powers, complete sequences, threshold of completeness
Article copyright: © Copyright 1975 American Mathematical Society