Primes of the form \([c^ p]\)
We combine techniques from multiplicative number theory and metrical number theory to prove that for almost all \(c>1\) the sequence \([c^p ]\), where \(p\) denotes a prime and \([\;]\) indicates integer part, contains infinitely many primes. We also show that the set of \(c>1\) for which \([c^n ]\) is never prime is uncountable.
distribution of primes in integer part sequences
scientific article; zbMATH DE number 861935