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- W2951674869 abstract "A set is said to be emph{3-free} if no three elements form an arithmetic progression. Given a 3-free set $A$ of integers $0=a_0 t$, we pick the smallest possible $a_n$ so that ${a_0,a_1,ldots,a_n}$ is 3-free and increasing. Work by Odlyzko and Stanley indicates that Stanley sequences may be divided into two classes. Sequences of Type 1 are highly structured and satisfy $alpha n^{log_2 3}/2le a_nle alpha n^{log_2 3}$, for some constant $alpha$, while those of Type 2 are chaotic and satisfy $Theta(n^2/log n)$. In this paper, we consider the possible values for $alpha$ in the growth of Type 1 Stanley sequences. Whereas Odlyzko and Stanley assumed $alpha=1$, we show that $alpha$ can be any rational number which is at least 1 and for which the denominator, in lowest terms, is a power of 3." @default.
- W2951674869 created "2019-06-27" @default.
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- W2951674869 date "2014-08-20" @default.
- W2951674869 modified "2023-09-27" @default.
- W2951674869 title "On the growth of Stanley sequences" @default.
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