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Sieve-Generated Sequences

Published online by Cambridge University Press:  20 November 2018

M. C. Wunderlich
M. C. Wunderlich*
Affiliation:
State University of New York, Buffalo
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We shall consider a generalization of the sieve process introduced by W. E. Briggs (1) in 1963. Let A(1) be the sequence {ak(1)}, where ak(1) = k + 1, so that A(1) = {2, 3, 4, … }. Suppose inductively that A(1), A(2), … , A(n) has been defined. 4(n+1) will be defined from A(n) = {a1(n), a2(n), a3(n), …} in the following manner: For each integer t ⩾ 0, choose an arbitrary element αt(n) from the set where an = an(n), and delete the elements αt(n) from A(n) to form A(n+1). The sequence A is defined to be the sequence {an}. It is also the set-theoretic intersection of all the sequences A(n), n — 1, 2, … . Let be the class of all sequences that can be generated by this sieve process.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 291 - 299
Copyright
Copyright © Canadian Mathematical Society 1966

References

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