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Bounded gaps between primes in special sequences


Authors: Lynn Chua, Soohyun Park and Geoffrey D. Smith
Journal: Proc. Amer. Math. Soc. 143 (2015), 4597-4611
MSC (2010): Primary 11N05, 11N36
Published electronically: May 22, 2015
MathSciNet review: 3391020
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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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Additional Information

Lynn Chua
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachu- setts Avenue, Cambridge, Massachusetts 02139
Email: chualynn@mit.edu

Soohyun Park
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 3 Ames Street, Cambridge, Massachusetts 02139
Email: soopark@mit.edu

Geoffrey D. Smith
Affiliation: Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, Connecticut 06511
Email: geoffrey.smith@yale.edu

DOI: https://doi.org/10.1090/proc/12607
Received by editor(s): July 7, 2014
Received by editor(s) in revised form: July 20, 2014
Published electronically: May 22, 2015
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2015 American Mathematical Society