Carmichael numbers composed of primes from a Beatty sequence

• Autorzy: William D. Banks , Aaron M. Yeager
• Języki publikacji: EN

Abstrakty

EN

Let α,β ∈ ℝ be fixed with α > 1, and suppose that α 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 $ℬ_{α,β} = (⌊αn + β⌋)_{n=1}^{∞}$. We conjecture that the same result holds true when α is an irrational number of infinite type.

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints
• 11B83: Special sequences and polynomials
• 11N13: Primes in progressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 1
• Strony: 129-137

Daty

wydano

2011

Twórcy

autor

William D. Banks

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

autor

Aaron M. Yeager

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/cm125-1-9