## A real recursion

### Problem 517

For every real number $a \gt 1$ is given the sequence $g_a$ by:

$g_{a}(x)=1$ for $x \lt a$

$g_{a}(x)=g_{a}(x-1)+g_a(x-a)$ for $x \ge a$

$G(n)=g_{\sqrt {n}}(n)$

$G(90)=7564511$.

Find $\sum G(p)$ for $p$ prime and $10000000 \lt p \lt 10010000$

Give your answer modulo 1000000007.