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A tough P1

Source: PRMO 2019 Leg 2 P1

August 25, 2019
number theoryPRMO

Problem Statement

Consider the sequence of numbers [n+2n+12]\left[n+\sqrt{2n}+\frac12\right], where [x][x] denotes the greatest integer not exceeding xx. If the missing integers in the sequence are n1<n2<n3<…n_1<n_2<n_3<\ldots find n12n_{12}
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