Consecutive primes and Beatty sequences
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DOI: 10.1016/j.jnt.2018.04.003
Abstract: Fix irrational numbers $\alpha,\hat\alpha>1$ of finite type and real numbers $\beta,\hat\beta\ge 0$, and let $B$ and $\hat B$ be the Beatty sequences $$ B:=(\lfloor\alpha m+\beta\rfloor)_{m\ge 1}\quad\text{and}\quad\hat B:=(\lfloor\hat\alpha m+\hat\beta\rfloor)_{m\ge 1}. $$ In this note, we study… read more here.
Keywords: beatty sequences; consecutive primes; hat alpha; primes beatty ... See more keywords