Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:application |
gptkb:Number_theory
Combinatorics |
| gptkbp:defines |
A Beatty sequence is a sequence of the form ⌊n·r⌋ for n = 1, 2, 3, ..., where r is an irrational number greater than 1.
|
| gptkbp:example |
For r = sqrt(2), the sequence is 1, 2, 4, 5, 7, 8, 10, ...
For r = golden ratio, the sequence is 1, 3, 4, 6, 8, 9, 11, ... |
| gptkbp:firstPublished |
1926
|
| gptkbp:form |
a_n = floor(n·r), where r > 1 and irrational
|
| https://www.w3.org/2000/01/rdf-schema#label |
Beatty sequence
|
| gptkbp:namedAfter |
gptkb:Samuel_Beatty
|
| gptkbp:OEIS |
A Beatty sequence can be found in OEIS for specific values of r, e.g., the golden ratio.
|
| gptkbp:property |
For irrational r > 1, the sequences ⌊n·r⌋ and ⌊n·s⌋, where 1/r + 1/s = 1, partition the set of positive integers.
|
| gptkbp:relatedTo |
gptkb:Sturmian_word
gptkb:Wythoff_sequence |
| gptkbp:bfsParent |
gptkb:Samuel_Beatty
|
| gptkbp:bfsLayer |
5
|