Carmichael numbers composed of primes from a Beatty sequence
Volume 125 / 2011
Colloquium Mathematicum 125 (2011), 129-137
MSC: Primary 11N25; Secondary 11N13, 11B83.
DOI: 10.4064/cm125-1-9
Abstract
Let $\alpha,\beta\in\mathbb R$ be fixed with $\alpha>1$, and suppose that $\alpha$ is irrational and of finite type. We show that there are infinitely many Carmichael numbers composed solely of primes from the non-homogeneous Beatty sequence $\mathscr B_{\alpha,\beta}=(\lfloor{\alpha n+\beta}\rfloor)_{n=1}^\infty$. We conjecture that the same result holds true when $\alpha$ is an irrational number of infinite type.
