Geodesic
Descriptions of the Characteristic Sequence of an Irrational
Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 15-21

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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.
DOI : 10.4153/CMB-1993-003-6
Mots-clés : 10L10 
Brown, Tom C. Descriptions of the Characteristic Sequence of an Irrational. Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 15-21. doi: 10.4153/CMB-1993-003-6
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