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A numerical sequence and a family of polynomials arising from a question of completeness

Published online by Cambridge University Press:  24 October 2008

L. E. Fraenkel
L. E. Fraenkel
Affiliation:
University of Sussex
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Extract

This paper concerns, in the first instance, a sequence {t(1), t(2), t(3), …} of positive numbers denned successively by

where k ∈ ℕ = {1,2,3,…} and

Thus, when k is odd, A(k) consists of those divisors of k that do not exceed k/3; when k is even, A (k) consists of those even divisors n of k that make k/n odd and do not exceed k/3. The sets A(k) are listed in Table 1 for k ≤ 105; the numbers t(1) to t(10) are 1, 1, 4/3, 1, 6/5, 4/3, 8/7, 1, 14/9, 6/5.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 3 , November 1980 , pp. 469 - 481
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

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