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On a question about sum-free sequences |
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| Authors: | Jean-Marc Deshouillers Paul Erd s Giuseppe Melfi |
| Institution: | a Mathématiques Stochastiques, Université Victor Segalen Bordeaux 2, F-33076, Bordeaux Cedex, France b Mathematical Institute of the Hungarian Academy of Sciences, Realtanoda u. 13–15, Pf. 127, H-1364, Budapest, Hungary c Dipartimento di Matematica, Università di Pisa, I-56127, Pisa, Italy |
| Abstract: | An increasing sequence of positive integers {n1, n2, …} is called a sum-free sequence if every term is never a sum of distinct smaller terms. We prove that there exist sum-free sequences {nk} with polynomial growth and such that limk→∞ nk+1/nk = 1. |
| Keywords: | Sum-free sequences Polynomial growth |
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