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c_{n+1} = [ 3/2 c_n ]

Source: Polish MO Recond Round 1989 p5

September 9, 2024
algebrarecurrence relationfloor functionnumber theory

Problem Statement

Given a sequence (cn) (c_n) of natural numbers defined recursively: c1=2 c_1 = 2 , cn+1=[32cn] c_{n+1} = \left[ \frac{3}{2}c_n\right] . Prove that there are infinitely many even numbers and infinitely many odd numbers among the terms of this sequence.
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