# Recurring Styles #11 - Smallest non-integral term of a Sequence!

Algebra Level 5

$\large{y_{n+1} = \dfrac12 \left( 3y_n + \sqrt{5 y_n^2 - 4} \right)}$

Define a sequence $$(y_n)_{n \geq 0}$$ by the above recurrence relation such that $$y_0 = 1, \ n \in \mathbb Z$$. Find the smallest value of $$n$$ such that $$y_n$$ is not an integer.

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