Fastest gap sequence for shell sort?

Question

According to Marcin Ciura's Optimal (best known) sequence of increments for shell sort algorithm, the best sequence for shellsort is 1, 4, 10, 23, 57, 132, 301, 701..., but how can I generate such a sequence? In Marcin Ciura's paper, he said:

Both Knuth’s and Hibbard’s sequences are relatively bad, because they are defined by simple linear recurrences.

but most algorithm books I found tend to use Knuth’s sequence: k = 3k + 1, because it's easy to generate. What's your way of generating a shellsort sequence?

Answer 1

Ciura's paper generates the sequence empirically -- that is, he tried a bunch of combinations and this was the one that worked the best. Generating an optimal shellsort sequence has proven to be tricky, and the problem has so far been resistant to analysis.

The best known increment is Sedgewick's, which you can read about here (see p. 7).