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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.
|Number of pages||14|
|Publication status||Published - 1 Mar 2016|
- Piatetski-Shapiro sequences
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- 1 Finished
New Applications of Additive Combinatorics in Number Theory and Graph Theory
Mans, B., Shparlinski, I., MQRES, M. & PhD Contribution (ARC), P. C.
1/01/14 → 31/12/17