Sums of distinct elements from a fixed set

Kløve, Torleiv

doi:10.1090/S0025-5718-1975-0398969-0

Sums of distinct elements from a fixed set
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Math. Comp. 29 (1975), 1144-1149 Request permission

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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