Note on the Reciprocal Sum of a Sum-Free Sequence |
Received:February 29, 2008 Revised:April 16, 2008 |
Key Words:
sum-free sequence reciprocal sum upper estimate.
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Fund Project:the Natural Science Foundation of the Education Department of Sichuan Province (No.2006C057). |
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Abstract: |
An infinite integer sequence $\{1\leq a_{1}< a_{2}< \cdots \} $ is called $A$-sequence, if no $a_{i}$ is sum of distinct members of the sequence other than $a_{i}$. We give an example for the $A$-sequence, and the reciprocal sum of elements is $\sum \frac{1}{a_{i}} > 2.065436491$, which improves slightly the related upper bounds for the reciprocal sums of sum-free sequences. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2009.04.023 |
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