Beatty Sequence
The Beatty sequence is a Spectrum Sequence with an Irrational base. In other words, theBeatty sequence corresponding to an Irrational Number 
is given by 
, 
,
, ..., where 
is the Floor Function. If 
and 
are PositiveIrrational Numbers such that
then the Beatty sequences
, 
, ... and 
, 
, ...together contain all the Positive Integers without repetition.
References
Gardner, M. Penrose Tiles and Trapdoor Ciphers...and the Return of Dr. Matrix, reissue ed. New York: W. H. Freeman, p. 21, 1989. Graham, R. L.; Lin, S.; and Lin, C.-S. ``Spectra of Numbers.'' Math. Mag. 51, 174-176, 1978. Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 227, 1994. Sloane, N. J. A. A Handbook of Integer Sequences. Boston, MA: Academic Press, pp. 29-30, 1973.
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