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mystical sequences x_{i+1} = [ x_i ] {x_i}

Source: 2021 Dürer Math Competition Finals Day 1 E4 E+2

January 2, 2022
floor functionSequencealgebra

Problem Statement

Indians find those sequences of non-negative real numbers x0,x1,...x_0, x_1,... mystical t hat satisfy x0<2021x_0 < 2021, xi+1=⌊xi⌋{xi}x_{i+1} = \lfloor x_i \rfloor \{x_i\} for every i≥0i \ge 0, furthermore the sequence contains an integer different from 00. How many sequences are mystical according to the Indians?
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