Geodesic
Determination of [nθ] by its Sequence of*Differences
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 441-446

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For any real number θ let where [x] denotes the greatest integer not exceeding x. A method is given for computing fθ from its first few terms. A similar method is given for computing the characteristic function gθ(n) of [nθ]. The given methods converge rapidly, and generalize previous results of Bernoulli, Markorf, and Stolarsky. Note that either of the sequences fθ and gθ determines the sequence [nθ] (n = 1, 2,...). 
Fraenkel, A. S.; Mushkin, M.; Tassa, U. Determination of [nθ] by its Sequence of*Differences. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 441-446. doi: 10.4153/CMB-1978-077-0
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     title = {Determination of [n\ensuremath{\theta}] by its {Sequence} {of*Differences}},
     journal = {Canadian mathematical bulletin},
     pages = {441--446},
     year = {1978},
     volume = {21},
     number = {4},
     doi = {10.4153/CMB-1978-077-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-077-0/}
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