Bounded gaps between primes in special sequences

TL;DR

This paper extends bounded prime gap results to special sequences derived from irrational numbers and functions, showing infinitely many bounded prime clusters within these sequences using advanced number theory methods.

Contribution

It introduces new results on bounded prime gaps within sequences of the form nlphand establishes the existence of bounded prime clusters in sequences defined by superlinear functions.

Findings

Bounded gaps between primes in sequences nlphare proven.

Existence of infinitely many bounded intervals with multiple primes in special sequences.

Primes appear in sequences defined by superlinear functions with specific properties.

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.