# Is the Legendre symbol with respect to a large prime usable as a pseudorandom generator?

Take an output length $\ell$ and a random seed $s \in \Bbb Z_p$ and a large 1000-bit or so prime number $p$ and output the Legendre symbols of $s, s+1, \dotsc, s + \ell - 1$ with respect to $p$.

There might be a vulnerability when $s$ is very close to $0$, so you need to give it a value sufficiently far away from $0$.

Is this a cryptographically secure pseudorandom generator? I can't seem to reduce it to any number theoretic problem.