Journal of Number Theory
First and Last Page
We address conjectures of P. Erdős 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 Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k,k2, k3,...,kr are simultaneously Sierpiński numbers.
Filaseta, M., Finch, C., & Kozek, M. (2008). On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture. Journal of Number Theory, 128(7), 1916-1940. https://doi.org/10.1016/j.jnt.2008.02.004