Journal of Integer Sequences, Vol. 10 (2007), Article 07.4.4

Variations on a Theme of Sierpiński

Lenny Jones
Department of Mathematics
Shippensburg University
Shippensburg, Pennsylvania 17257


Using an idea of Erdős, Sierpiński proved that there exist infinitely many odd positive integers k such that k•2n+1 is composite for all positive integers n. In this paper we give a brief discussion of Sierpiński's theorem and some variations that have been examined, including the work of Riesel, Brier, Chen, and most recently, Filaseta, Finch and Kozek. The majority of the paper is devoted to the presentation of some new results concerning our own variations of Sierpiński's original theorem.

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Received November 14 2006; revised version received April 14 2007. Published in Journal of Integer Sequences, April 14 2007.

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