Iterated Floor Function, Algebraic Numbers, Discrete Chaos, Beatty Subsequences, Semigroups
Iterated Floor Function, Algebraic Numbers, Discrete Chaos, Beatty Subsequences, Semigroups
For a real number a, the floor function |aj is the integer part of a .The sequence {\ma\ : m = 1,2,3,...} is the Beatty sequence of a .Identities are proved which express the sum of the iterated floor functional A' for \ < i < n , operating on …