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Bounded expansive sequences

Source: KöMaL A. 713

February 13, 2018
algebraSequencepositive

Problem Statement

We say that a sequence a1,a2,⋯a_1,a_2,\cdots is expansive if for all positive integers j,  i<jj,\; i<j implies ∣ai−aj∣≥1j|a_i-a_j|\ge \tfrac 1j. Find all positive real numbers CC for which one can find an expansive sequence in the interval [0,C][0,C].
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