Nested sqrt

We have

$\sqrt{2013+276\sqrt{2027+278\sqrt{2041+280\sqrt{2055+\ldots}}}} \\ = \sqrt{(7)(276)+ (9)^2 +276\sqrt{(7)(276+2) + (9)^2 + (276+2)\sqrt{(7)(276+2\times 2) + (9)^2 +(276+2\times 2)\sqrt{\ldots}}}}$

which can be compared to Ramanujan's infinite nested radical function

$F(n,a,x) = \sqrt{ax + (a+n)^2 + x \sqrt{ a(x+n) + (a+n)^2 + (x+n) \sqrt{ a(x+2n) + (a+n)^2 + (x+2n) \sqrt{\ldots}}}}$

to get $a=7, n=2, x=276$ . The answer to the infinite nested radical function is $F(n,a,x) = n+a+x$ giving us the answer as $2+7+276 = \boxed{285}$ .