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We address conjectures of P. Erd˝ os and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpi´nski number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k, k 2 , k 3 ,. ..(More)
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