Sums of distinct elements from a fixed set

Author:
Torleiv KlĂ¸ve

Journal:
Math. Comp. **29** (1975), 1144-1149

MSC:
Primary 10A40; Secondary 10B35

DOI:
https://doi.org/10.1090/S0025-5718-1975-0398969-0

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0398969-0

Keywords:
Sums of distinct integers,
sums of powers,
complete sequences,
threshold of completeness

Article copyright:
© Copyright 1975
American Mathematical Society