Number of consecutive nonzero quadratic residues modulo an odd prime
= Number of consecutive nonzero quadratic residues modulo an odd prime
The number of $z\in\{1,\ldots,p-2\}$ for which both $z$ and $z+1$ are quadratic residues modulo $p$ is
$$
\frac{p-4-(-1)^{(p-1)/2}}4.
$$