Sequences and series involving the sequence of composite numbers

Panayiotis Vlamos

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-6

Abstract:

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 ≥ 1 , defined by x n = ∑ k = 1 n ( c k + 1 − c k ) / k − p n / n , and the series ∑ n = 1 ∞ ( p c n − c p n ) / n p n are convergent.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:196815

DOI: 10.1155/S016117120201284X

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