Bounded gaps between primes in special sequences

Chua, Lynn; Park, Soohyun; Smith, Geoffrey

doi:10.1090/proc/12607

Bounded gaps between primes in special sequences
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by Lynn Chua, Soohyun Park and Geoffrey D. Smith PDF

Proc. Amer. Math. Soc. 143 (2015), 4597-4611 Request permission

Abstract:

We use Maynard’s methods to show that there are bounded gaps between primes in the sequence $\{\lfloor n\alpha \rfloor \}$, where $\alpha$ is an irrational number of finite type. In addition, given a superlinear function $f$ satisfying some properties described by Leitmann, we show that for all $m$ there are infinitely many bounded intervals containing $m$ primes and at least one integer of the form $\lfloor f(q)\rfloor$ with $q$ a positive integer.

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