Sequences and series involving the sequence of composite numbers (Q1607914)
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scientific article; zbMATH DE number 1780398
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sequences and series involving the sequence of composite numbers |
scientific article; zbMATH DE number 1780398 |
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Sequences and series involving the sequence of composite numbers (English)
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13 August 2002
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Summary: Denoting by \(p_{n}\) and \(c_{n}\) the \(n\)th prime number and the \(n\)th composite number, respectively, we prove that both the sequence \((x_{n})_{n\geq 1}\), defined by \(x_{n}=\sum _{k=1}^n (c_{k+1}-c_{k})/k-p_{n}n\), and the series \[ \sum_{n=1}^\infty (p_{c_{n}}-c_{p_{n}})/np_{n} \] are convergent.
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