With t random integers revealed, buying Θ((n/t)^((k−2)/2)) of them is necessary and sufficient to guarantee a k-term arithmetic progression when t ≫ n^(1−2/k).
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Arithmetic progressions in a random set on a budget
With t random integers revealed, buying Θ((n/t)^((k−2)/2)) of them is necessary and sufficient to guarantee a k-term arithmetic progression when t ≫ n^(1−2/k).