Geodesic
Some Properties of Beatty Sequences I*
Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 190-197

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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. 
Connell, Ian G. Some Properties of Beatty Sequences I*. Canadian mathematical bulletin, Tome 2 (1959) no. 3, pp. 190-197. doi: 10.4153/CMB-1959-025-0
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     title = {Some {Properties} of {Beatty} {Sequences} {I*}},
     journal = {Canadian mathematical bulletin},
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     year = {1959},
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     doi = {10.4153/CMB-1959-025-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-025-0/}
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