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Determine x_1997 in recursive sequence

Source: Baltic Way 1997

January 28, 2011
floor functionalgebra proposedalgebra

Problem Statement

Let x1=1x_1=1 and xn+1=xn+⌊xnn⌋+2x_{n+1} =x_n+\left\lfloor \frac{x_n}{n}\right\rfloor +2, for n=1,2,3,…n=1,2,3,\ldots where xx denotes the largest integer not greater than xx. Determine x1997x_{1997}.
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