BOUNDED GAPS BETWEEN PRIMES IN SPECIAL SEQUENCES

摘要

We use Maynard's methods to show that there are bounded gaps between primes in the sequence {[n alpha]}, where a 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 [f(q)] with q a positive integer.