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Non-decresing sequence of consecutive positive integers

Source: Czech and Slovak Olympiad 1961, National Round, Problem 1

June 16, 2024
Sequenceconsecutivepositive integers

Problem Statement

Consider an infinite sequence 1,2,2,3,3,3,4,4,4,4,5,…,n,…,n⏟n times,….1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, \ldots, \underbrace{n,\ldots,n}_{n\text{ times}},\ldots. Find the 1000th term of the sequence.
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