Almost primes of the form ⌊pc

William D. Banks, Victor Z. Guo, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Let Pc=(⌊pc⌋)p∈P with c> 1 and c∉N, where P is the set of prime numbers, and ⌊. ⌋ is the floor function. We show that for every such c there are infinitely many members of Pc having at most R(c) prime factors, giving explicit estimates for R(c) when c is near one and also when c is large.

Original languageEnglish
Pages (from-to)423-436
Number of pages14
JournalIndagationes Mathematicae
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Mar 2016
Externally publishedYes

Keywords

  • Piatetski-Shapiro sequences
  • Primes

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