A special subset of spectrum sequences, which use an irrational number as the spectrum base. Using the base *k*, the sequence is therefore:

[k], [2k], [3k], ...

where [ ] is the floor function.

A special property of any Beatty sequence is that, if we pick two bases *a* and *b* such that

1 1
--- + --- = 1
a b

Then the Beatty sequences with *a* and *b* as bases contain between them all the natural numbers, without duplication! I'm unsure of the proof for this, but I shall look into it.