Descriptions of the Characteristic Sequence of an Irrational
Descriptions of the Characteristic Sequence of an Irrational
复制标题
无理数特征序列的描述
DOI：
10.4153/cmb-1993-003-6
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
T. Brown
中科院分区：
文献类型：
--
作者：
T. Brown
Abstract Let α be a positive irrational real number. (Without loss of generality assume 0 < α < 1.) The characteristic sequence of α is f(α) =f1f2 ···, where fn = [(n + 1)α] - [nα]. We make some observations on the various descriptions of the characteristic sequence of α which have appeared in the literature. We then refine one of these descriptions in order to obtain a very simple derivation of an arithmetic expression for [nα] which appears in A. S. Fraenkel, J. Levitt, and M. Shimshoni [17]. Some concluding remarks give conditions on n which are equivalent to fn = 1.
