Prime numbers with Beatty sequences

William D. Banks, Igor E. Shparlinski

Type: Article

Publication Date: 2009-01-01

Citations: 52

DOI: https://doi.org/10.4064/cm115-2-1

Abstract

A study of certain Hamiltonian systems has led Y. Long to conjecture the existence of infinitely many primes which are not of the form $p=2\lfloor \alpha n\rfloor +1$, where $1< \alpha < 2$ is a fixed irrational number. An argument of P. Ribenboim coupl

Locations

Colloquium Mathematicum - View - PDF
arXiv (Cornell University) - View - PDF

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Action	Title	Year	Authors
+	Primes with Beatty and Chebotarev conditions	2020	Caleb Ji Joshua Kazdan Vaughan McDonald
+ PDF Chat	Arithmetic functions on Beatty sequences	2008	Alex G. Abercrombie William D. Banks Igor E. Shparlinski
+ PDF Chat	Strings of special primes in arithmetic progressions	2013	Keenan Monks Sarah Peluse Lynnelle Ye
+	Bounded gaps between primes in special sequences	2014	Lynn Chua Soo-Hyun Park G. Smith
+	Residue pattern for infinitely many primes	2022	C. G. Karthick Babu Anirban Mukhopadhyay A. Sankaranarayanan
+	Irregularities in the Distribution of Prime Numbers in a Beatty Sequence	2019	Janyarak Tongsomporn Jörn Steuding
+ PDF Chat	k-Free numbers and integer parts of αp	2022	Şermin ÇAM ÇELİK
+	Biases amongst products of two Beatty primes in arithmetic progressions	2024	Walid Wannes
+ PDF Chat	Beatty primes from fractional powers of almost-primes	2023	Victor Zhenyu Guo Jinjiang Li Min Zhang
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Works Cited by This (31)

Action	Title	Year	Authors
+	The New Book of Prime Number Records	1996	Paulo Ribenboim
+ PDF Chat	The Distribution of Prime Numbers	1933	A. E. Ingham
+	Approximation by algebraic numbers	2006	Yann Bugeaud
+	The Method of Trigonometrical Sums in the Theory of Numbers	2004	Ivan Matveevich Vinogradov K. F. Roth Anne Ashley Davenport
+	Uniform distribution of sequences	1974	L. Kuipers Harald Niederreiter
+	Prime divisors in Beatty sequences	2006	William D. Banks Igor E. Shparlinski
+ PDF Chat	Arithmetic functions on Beatty sequences	2008	Alex G. Abercrombie William D. Banks Igor E. Shparlinski
+ PDF Chat	Exponential sums over primes in an arithmetic progression	1985	Antal Balog Alberto Perelli
+	Primzahlen der Gestalt [f(n)]	1975	Dieter Leitmann Dieter Wolke
+ PDF Chat	On a conjecture of Yiming Long	2006	Chaohua Jia