International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 31-36

Sequences and series involving the sequence of composite numbers

Panayiotis Vlamos

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.


Denoting by pn and cn the nth prime number and the nth composite number, respectively, we prove that both the sequence (xn)n1, defined by xn=k=1n(ck+1ck)/kpn/n, and the series n=1(pcncpn)/npn are convergent.