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19th kmo #3

Source: KMO round 2, problem 3

February 3, 2006
number theory unsolvednumber theory

Problem Statement

For a positive integer KK, define a sequence, {an}n\{a_n\}_n, as following a1=Ka_1=K, a_{n+1} = \{ \begin{array} {cc} a_n-1 , & \mbox{ if } a_n \mbox{ is even} \\ \frac{a_n-1}2 , & \mbox{ if } a_n \mbox{ is odd} \end{array}, for all n≥1n\geq 1. Find the smallest value of KK, which makes a2005a_{2005} the first term equal to 0.
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