Define a sequence \left\{a_{n}\right\}_{n=1}^{\infty} via a_{1}=1 and a_{n+1}=a_{n}+\left\lfloor\sqrt{a_{n}}\right\rfloor for all n \geq 1. What is the smallest N such that a_{N}>2017?
Define a sequence \left\{a_{n}\right\}_{n=1}^{\infty} via a_{1}=1 and a_{n+1}=a_{n}+\left\lfloor\sqrt{a_{n}}\right\rfloor for all n \geq 1. What is the smallest N such that a_{N}>2017?