Don't write all the possibilities, part 2

Algebra Level 5

Given \( y=\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-\ldots}}}}\), within the range \( 1 \leq y \leq 2015\):

Given that \(x\) is a natural number such that \( 1 \leq y \leq 2015\), what is the probability that \(y\) is a natural number?

Express the probability in the form \(\dfrac{a}{b}\) (fraction in simplest form), and enter into the answer box the value of \(a+b\).

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