Carmichael numbers composed of primes from a Beatty sequence

William D. Banks; Aaron M. Yeager

Carmichael numbers composed of primes from a Beatty sequence

William D. Banks; Aaron M. Yeager

Colloquium Mathematicae (2011)

Volume: 125, Issue: 1, page 129-137
ISSN: 0010-1354

Access Full Article

top

Access to full text

Full (PDF)

Abstract

top

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} = {(⌊ α n + β ⌋)}_{n = 1}^{\infty}

. We conjecture that the same result holds true when α is an irrational number of infinite type.

How to cite

top

MLA
BibTeX
RIS

William D. Banks, and Aaron M. Yeager. "Carmichael numbers composed of primes from a Beatty sequence." Colloquium Mathematicae 125.1 (2011): 129-137. <http://eudml.org/doc/284092>.

@article{WilliamD2011,
abstract = {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.},
author = {William D. Banks, Aaron M. Yeager},
journal = {Colloquium Mathematicae},
keywords = {Carmichael numbers; Beatty sequences},
language = {eng},
number = {1},
pages = {129-137},
title = {Carmichael numbers composed of primes from a Beatty sequence},
url = {http://eudml.org/doc/284092},
volume = {125},
year = {2011},
}

TY - JOUR
AU - William D. Banks
AU - Aaron M. Yeager
TI - Carmichael numbers composed of primes from a Beatty sequence
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 1
SP - 129
EP - 137
AB - 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.
LA - eng
KW - Carmichael numbers; Beatty sequences
UR - http://eudml.org/doc/284092
ER -

Citations in EuDML Documents

top

Wei Zhang, On $k$ -free numbers over Beatty sequences

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.