Joel E. Iiams

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For an integer b ≥ 2 and for x ∈ [0, 1), define ρb(x) = ∑∞ n=0 {{bx}} bn , where {{t}} denotes the fractional part of the real number t. A number of properties of ρb are derived, and then a connection between ρb and the rumor conjecture is established. To form a rumor sequence {zn}, first select integers b ≥ 2 and k ≥ 1. Then select an integer z0, and for n(More)
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