International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 539-544
On the -th extension of the Sieve of eratosthenes
Department of Mathematical Sciences, The University of Akron, Akron 44325-4002, OH, USA
Received 19 November 1993; Revised 28 March 1994
Copyright © 1995 Antonio R. Quesada. 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.
The Sieve of Eratosthenes has been recently extended by excluding the multiples
of 2, 3, and 5 from the initial set, and finding the additive rules that give the positions of the
multiples of the remaining primes. We generalize these results. For a given we let the initial
set consists of natural numbers relatively prime to the first primes, and find the rules
governing the positions of the multiples of the remaining elements.