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- W4299562709 abstract "Fix irrational numbers $alpha,hatalpha>1$ of finite type and real numbers $beta,hatbetage 0$, and let $B$ and $hat B$ be the Beatty sequences $$ B:=(lflooralpha m+betarfloor)_{mge 1}quadtext{and}quadhat B:=(lfloorhatalpha m+hatbetarfloor)_{mge 1}. $$ In this note, we study the distribution of pairs $(p,p^sharp)$ of consecutive primes for which $pin B$ and $p^sharpinhat B$. Under a strong (but widely accepted) form of the Hardy-Littlewood conjectures, we show that $$ big|{ple x:pin Btext{ and }p^sharpinhat B}big|=(alphahatalpha)^{-1}pi(x)+Obig(x(log x)^{-3/2+epsilon}big), $$ where $pi(x)$ is the prime counting function." @default.
- W4299562709 created "2022-10-02" @default.
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- W4299562709 date "2016-12-05" @default.
- W4299562709 modified "2023-09-27" @default.
- W4299562709 title "Consecutive primes and Beatty sequences" @default.
- W4299562709 doi "https://doi.org/10.48550/arxiv.1612.01468" @default.
- W4299562709 hasPublicationYear "2016" @default.
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