Consecutive moderate gaps between zeros of the Riemann zeta function

Let $0<{\gamma }_1\le {\gamma }_2\le \cdots$ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts. For $c>0$ fixed (but possibly small), $T$ large, and ${\gamma }_n\le T$, we call a gap ${\gamma }_{n+1}-{\gamma }_n$ between consecutive ordinates ``moderate’’ if ${\gamma }_{n+1}-{\gamma }_n\ge 2\pi c\mathrm{/}\log T$. We investigate whether infinitely often there exists $r$ consecutive moderate gaps between ordinates ${\gamma }_{n+1}-{\gamma }_n,{\gamma }_{n+2}-{\gamma }_{n+1},\dots ,{\gamma }_{n+r}-{\gamma }_{n+r-1}$.