OFFSET
1,2
COMMENTS
The gaps were found empirically using a generalization of the formula which generates Tokuda's good gaps (A108870). These are a noticeable improvement over Tokuda's sequence when sorting random data, especially where N is in the millions.
The specific gamma = 2.243609061420001 is used to generate the present sequence. If one were to continue the search for a better gamma, the next best value lies within the range: 2.243609055217999... < gamma <= 2.243609061420001...
LINKS
Ying Wai Lee, Empirically Improved Tokuda Gap Sequence in Shellsort, arXiv:2112.11112 [cs.DS], 2021.
FORMULA
a(n) = ceiling((gamma^n - 1)/(gamma - 1)), where gamma = 2.243609061420001
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Stephen J. Chick, Oct 17 2023
STATUS
approved