Polynomially growing integer sequences all whose terms are composite

TL;DR

This paper characterizes specific polynomially growing integer sequences, defined by the floor of n^t divided by d, that contain only finitely many prime numbers, expanding understanding of prime distribution in such sequences.

Contribution

It identifies all pairs of positive integers (t, d) for which the sequence loor n^t/d ontains finitely many primes, providing a complete classification.

Findings

Characterization of pairs (t, d) with finitely many primes in the sequence

Complete classification of polynomial sequences with limited prime terms

Insights into prime distribution in polynomial floor sequences

Abstract

We identify pairs of positive integers $(t, d)$ with the property that the integer sequence with general term $\lfloor{n^t/d\rfloor}$ contains at most finitely many primes.