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On Langford’s Problem (I)

Published online by Cambridge University Press:  03 November 2016

C. J Priday
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For numbers a ≥ b ≥ l we shall denote by (a, b) the set of numbers b, b + 1, …, a. We shall say that a set S of numbers is perfect if there exists a sequence containing just one pair of each of the numbers in S, satisfying the condition: for every number r in the set, the two r’s are separated by exactly r places, and having no gaps (a perfect sequence).

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Type
Research Article
Information
The Mathematical Gazette , Volume 43 , Issue 346 , December 1959 , pp. 250 - 253
Copyright
Copyright © Mathematical Association 1959

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References

page 250 of note * The writing of this paper is part of the work made possible by a grant from the Carnegie Corporation of New York for the development of the author’s approach to mathematics.

page 253 of note † These are proved in the paper which follows.

page 253 of note ‡ Th. Skolem. On certain disturbution of integers in pairs with given differences. Math. Scand. 5 (1957), 57-68.