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When Does Appending the Same Digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers?

Lenny Jones
The American Mathematical Monthly
Vol. 118, No. 2 (February 2011), pp. 153-160
DOI: 10.4169/amer.math.monthly.118.02.153
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.118.02.153
Page Count: 8
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When Does Appending the Same Digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers?
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Abstract

Abstract Let k be a positive integer, and suppose that k = a1a2 . . . at, where ai is the ith digit of k (reading from left to right). Let d ∈ {0,1,…,9}. For n ≥ 1, define \documentclass{article}\pagestyle{empty}\begin{document}$$s_n = a_1 a_2 \ldots a_t \underbrace{dd\ldots d}_n.$$\end{document} In this article, we examine when sn is composite for all n.

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