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2017 A9: Sequence of Floors and Square Roots

Source:

January 29, 2017
2017algebra

Problem Statement

Define a sequence {an}n=1∞\{a_{n}\}_{n=1}^{\infty} via a1=1a_{1} = 1 and an+1=an+⌊an⌋a_{n+1} = a_{n} + \lfloor \sqrt{a_{n}} \rfloor for all n≥1n \geq 1. What is the smallest NN such that aN>2017a_{N} > 2017?
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