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IMO ShortList 1998, number theory problem 4

Source: IMO ShortList 1998, number theory problem 4

October 22, 2004

number theoryInteger sequenceCalculateIMO Shortlist

Problem Statement

A sequence of integers

a_{1},a_{2},a_{3},\ldots

is defined as follows: a_{1} \equal{} 1 and for

n\geq 1

, a_{n \plus{} 1} is the smallest integer greater than

a_{n}

such that a_{i} \plus{} a_{j}\neq 3a_{k} for any

i,j

and

k

in \{1,2,3,\ldots ,n \plus{} 1\}, not necessarily distinct. Determine

a_{1998}