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The Composite Two-Step
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Eric Kaper

Department of Mathematics

University of Kentucky

Lexington, KY 40506

USA

Ryan Stuffelbeam

Mathematics Program

Transylvania University

Lexington, KY 40508

USA

**Abstract:**

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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