International Journal of Mathematics and Mathematical Sciences 
Volume 18 (1995), Issue 3, Pages 539-544
doi:10.1155/S0161171295000688

On the K-th extension of the Sieve of eratosthenes

Antonio R. Quesada

 Department of Mathematical Sciences, The University of Akron, Akron 44325-4002, OH, USA
Received 19 November 1993; Revised 28 March 1994

Abstract

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 k we let the initial set Sk consists of natural numbers relatively prime to the first k primes, and find the rules governing the positions of the multiples of the remaining elements.