Journal of Integer Sequences, Vol. 20 (2017), Article 17.9.1

The Composite Two-Step

Eric Kaper
Department of Mathematics
University of Kentucky
Lexington, KY 40506

Ryan Stuffelbeam
Mathematics Program
Transylvania University
Lexington, KY 40508


Let a be a nonzero digit and b any of the digits 1, 3, 7, or 9. To a positive integer k, we alternately append a on the left and b on the right. This process yields two infinite sequences of integers, depending on which side the appending process begins. We are interested in those values of k that result in these sequences being composed entirely of composite integers. In particular, we seek the smallest such k relatively prime to the greatest common divisor of a and b.

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Received March 2 2017; revised versions received September 4 2017; September 6 2017. Published in Journal of Integer Sequences, September 8 2017.

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