Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).

Filaseta, Michael and Finch, Carrie and Kozek, Mark, On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture. J. Number Theory 128 (2008), no. 7, 1916-1940.

Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; doi:10.1007/978-0-387-26677-0. Section B21 "$k\cdot2^n+1$ composite for all $n$", pp. 119--121, gives Sierpiński's covering-congruence construction, Selfridge's $78557$ and Stanton's covering sets for $k\cdot2^n-1$, and does not state the question; the site's commentary locates its precise formulation in Guy's problem F13. Section F13 "Covering systems of congruences" (from p. 382) records on p. 384 Erdős's conjecture that every sequence $d\cdot2^k+1$ ($k=1,2,\dots$), $d$ fixed and odd, that contains no primes can be obtained from covering congruences, equivalently that the least prime factors of its terms are bounded. Library home: Guy 2004.

Izotov, Anatoly S., A note on Sierpiński numbers. Fibonacci Quart. (1995), 206-207.

Sierpiński, W., Sur un problème concernant les nombres $k\cdot 2\sp{n}+1$. Elem. Math. (1960), 73-74.