  Experiments are conducted to improve Tokuda (1992) gap sequence in Shellsort
into $\gamma$-sequences, and the best result is the gap sequence in which the
$k$-th increment $h_k$ is given by \begin{align} h_k=\left\lceil
\frac{\gamma^k-1}{\gamma-1} \right\rceil \end{align} , where
$\gamma=2.243609061420001...$ and $k\in\mathbb{N}_1$. The first few increments
of the gap sequence are \begin{align} 1,\, 4,\, 9,\, 20,\, 45,\, 102,\, 230,\,
516,\,1158,\,2599,\,5831,\,13082,\,29351,\,65853,\, 147748,\,331490,\,743735,\,
...\end{align}It empirically yields less numbers of comparison on average than
Tokuda (1992) gap sequence. In the procedure of search, it reveals the
potential existence of a new type of fractal.
