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arXiv · 2305.09219

Generalized Sierpi\'nski Numbers

Michael Filaseta·Robert Groth·Thomas Luckner
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Abstract

A Sierpi\'nski number is a positive odd integer $k$ such that $k \cdot 2^n + 1$ is composite for all positive integers $n$. Fix an integer $A$ with $2 \le A$. We show that there exists a positive odd integer $k$ such that $k\cdot a^n + 1$ is composite for all integers $a \in [2, A]$ and all $n \in \mathbb{Z}^+$.

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Michael Filaseta, Robert Groth, Thomas Luckner. 2023-05-16. Generalized Sierpi\'nski Numbers. https://arxiv.org/abs/2305.09219

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