Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.1

Polygonal, Sierpiński, and Riesel Numbers


Daniel Baczkowski and Justin Eitner
Department of Mathematics
The University of Findlay
Findlay, OH 45840
USA

Carrie E. Finch and Braedon Suminski
Department of Mathematics
Washington and Lee University
Lexington, VA 24450
USA

Mark Kozek
Department of Mathematics
Whittier College
Whittier, CA 90608
USA

Abstract:

In this paper, we show that there are infinitely many Sierpiński numbers in the sequence of triangular numbers, hexagonal numbers, and pentagonal numbers. We also show that there are infinitely many Riesel numbers in the same sequences. Furthermore, we show that there are infinitely many n-gonal numbers that are simultaneously Sierpiński and Riesel.

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(Concerned with sequences A000217 A000290 A000326 A000384 A180247.)

Received November 25 2014; revised version received June 19 2015; July 9 2015. Published in Journal of Integer Sequences, July 16 2015.

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