International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 131-134
Gaps in the sequence
Department of Mathematics, Santa Clara University, Santa Clara 95053, CA, USA
Received 16 September 1985
Copyright © 1987 Vladimir Drobot. 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.
Let be an irrational number and let denote the fractional part of . For each let be the intervals resulting from the partition of by the points , . Let be the number of distinct lengths these intervals can assume. It is shown that . This is in contrast to the case of the sequence , where .