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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 1, Pages 75-85
http://dx.doi.org/10.1155/S0161171296000129

Further results on a generalization of Bertrand's postulate

Department of Mathematics, Physics and Computer Science, Ryerson Polytechnic University, Ontario, Toronto M5B 2K3, Canada

Received 6 November 1992; Revised 28 February 1995

Copyright © 1996 Hindawi Publishing Corporation. 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

Let d(k) be defined as the least positive integer n for which pn+1<2pnk. In this paper we will show that for k286664, then d(k)<k/(logk2.531) and for k2, then k(11/logk)/logk<d(k). Furthermore, for k sufficiently large we establish upper and lower bounds for d(k).