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Sieve-Generated Sequences with Translated Intervals

Published online by Cambridge University Press:  20 November 2018

R. G. Buschman  and
M. C. Wunderlich
R. G. Buschman
Affiliation:
State University of New York, Buffalo
M. C. Wunderlich
Affiliation:
State University of New York, Buffalo
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Consider the following sieve process. Let A(1) be the sequence of integers greater than 1. Let A(n+1) be obtained from A(n) = {a1(n), a2(n), …} by eliminating one element from each of the intervals Ik(n), where

We let an = an(n) and A = {an} be the sequence of integers that survive the sieve. M. C. Wunderlich (8) has found a necessary and sufficient condition for an ∼ n log n and, in a more recent paper, M. Wunderlich and W. E. Briggs (9) have studied a subclass of the sequences defined above for which an ∼ n log n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 559 - 570
Copyright
Copyright © Canadian Mathematical Society 1967

References

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