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On the Average Asymptotic Behavior of a Certain Type of Sequence of Integers
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Bakir Farhi
Published/Copyright:
November 25, 2009
Abstract
In this paper, we prove the following result: Let 
be an infinite set of positive integers. For all positive integers n, let τn denote the smallest element of which does not divide n. Then we have
In the two particular cases when is the set of all positive integers and when is the set of the prime numbers, we give a more precise result for the average asymptotic behavior of (τn)n. Furthermore, we discuss the irrationality of the limit of τn (in the average sense) by applying a result of Erdős.
Keywords.: Special sequences of integers; convergence in the average sense; least common multiple; irrational numbers
Received: 2008-10-12
Revised: 2009-04-14
Accepted: 2009-05-18
Published Online: 2009-11-25
Published in Print: 2009-November
© de Gruyter 2009
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Keywords for this article
Special sequences of integers;
convergence in the average sense;
least common multiple;
irrational numbers
Articles in the same Issue
- An Analogue of the Erdős–Ginzburg–Ziv Theorem for Quadratic Symmetric Polynomials
- Counting Determinants of Fibonacci–Hessenberg Matrices Using LU Factorizations
- A Short Proof of a Series Evaluation in Terms of Harmonic Numbers
- Generalization of an Identity Involving the Generalized Fibonacci Numbers and Its Applications
- Inductive Methods and Zero-Sum Free Sequences
- On the Number of Zero-Sum Subsequences of Restricted Size
- On the Average Asymptotic Behavior of a Certain Type of Sequence of Integers
- On the Kernel of the Coprime Graph of Integers
- Bell Numbers and Variant Sequences Derived from a General Functional Differential Equation
- Balanced Subset Sums in Dense Sets of Integers
- Some Results for Generalized Harmonic Numbers
