MathDB

N1

Part of 2015 IMO Shortlist

Problems(1)

Floor sequence

Source: 2015 ISL N1

7/7/2016
Determine all positive integers MM such that the sequence a0,a1,a2,⋯a_0, a_1, a_2, \cdots defined by a_0 = M + \frac{1}{2} \qquad \textrm{and} \qquad a_{k+1} = a_k\lfloor a_k \rfloor   \textrm{for} \, k = 0, 1, 2, \cdots contains at least one integer term.
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