MathDB
How long before a function with g(n+1)=g(n)+-1 reaches 2001

Source: XII Cono Sur Mathematical Olympiad (2001)

July 28, 2011
functioninductionalgebra unsolvedalgebra

Problem Statement

A function gg defined for all positive integers nn satisfies [*]g(1)=1g(1) = 1; [*]for all n≥1n\ge 1, either g(n+1)=g(n)+1g(n+1)=g(n)+1 or g(n+1)=g(n)−1g(n+1)=g(n)-1; [*]for all n≥1n\ge 1, g(3n)=g(n)g(3n) = g(n); and [*]g(k)=2001g(k)=2001 for some positive integer kk. Find, with proof, the smallest possible value of kk.
Back to ProblemsView on AoPS