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Some Properties of Beatty Sequences I*

Published online by Cambridge University Press:  20 November 2018

Ian G. Connell
Ian G. Connell*
Affiliation:
C.A.R.D.E. , Quebec
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Two sequences of natural numbers are said to be complementary if they contain all the positive integers without repetition or omission. S. Beatty [l] observed that the sequences

(1)

(2)

(where square brackets denote the integral part function) are complementary if and only if α > 0 and α is irrational. We call the pair (1),(2) Beatty sequences of argument α.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 3 , 01 September 1959 , pp. 190 - 197
Copyright
Copyright © Canadian Mathematical Society 1959

Footnotes

*

Excerpt from Master of Science thesis, University of Manitoba, 1959.

References

1. Beatty, S., Amer. Math. Monthly, 33 (1926), 159 (problem); solutions, ibid., 34(1927), 159.Google Scholar
2. Connell, I.G., A generalization of Wythoff's game, Can. Math. Bull. 2 (1959),Google Scholar
3. Sierpinski, W., Bull. Inter. Acad. Sc., Cracovie, 11(1909), 725-727.Google Scholar