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We denote $A = \\{a_{1}, a_{2}, \\dots{}\\}$ defined by the following greedy algorithm: if $l \\ge t$ and $a_{1}, \\dots{}, a_{l}$ have already been defined, then $a_{l+1}$ is the smallest integer $a > a_{l}$ such that $\\{a_{1}, \\dots{}, a_{l}\\} \\cup \\{a\\}$ also does not contain a $k$-term arithmetic progression. 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Kiss","submitted_at":"2017-10-05T09:37:53Z","abstract_excerpt":"Let $\\mathbb{N}$ denote the set of all nonnegative integers. Let $k\\ge 3$ be an integer and $A_{0} = \\{a_{1}, \\dots{}, a_{t}\\}$ $(a_{1} < \\ldots< a_{t})$ be a nonnegative set which does not contain an arithmetic progression of length $k$. We denote $A = \\{a_{1}, a_{2}, \\dots{}\\}$ defined by the following greedy algorithm: if $l \\ge t$ and $a_{1}, \\dots{}, a_{l}$ have already been defined, then $a_{l+1}$ is the smallest integer $a > a_{l}$ such that $\\{a_{1}, \\dots{}, a_{l}\\} \\cup \\{a\\}$ also does not contain a $k$-term arithmetic progression. 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