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In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are named after Samuel Beatty, who wrote about them in 1926. Rayleigh's theorem, named after Lord Rayleigh, states that the complement of a Beatty sequence, consisting of the positive integers that are not in the sequence, is itself a Beatty sequence generated by a different irrational number. Beatty sequences can also be used to generate Sturmian words. ==Definition== A positive irrational number generates the Beatty sequence : If then is also a positive irrational number. They naturally satisfy : and the sequences : and : form a ''pair of complementary Beatty sequences''. A more general non-homogeneous Beatty sequence takes the form : where is a real number. For , the complementary non-homogeneous Beatty sequences can be found by making so that : and : form a pair of complementary Beatty sequences. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Beatty sequence」の詳細全文を読む スポンサード リンク
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