International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 31-36
doi:10.1155/S016117120201284X
Sequences and series involving the sequence of composite numbers
Hellenic Open University, Patras, Greece
Received 17 April 2001; Revised 2 October 2001
Copyright © 2002 Panayiotis Vlamos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Denoting by pn and cn the nth prime number and the nth composite number, respectively, we prove that both the sequence (xn)n≥1, defined by xn=∑k=1n (ck+1−ck) / k−pn / n, and the series ∑n=1∞ (pcn−cpn) / npn are convergent.