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A366726
Lee's empirically improved Tokuda gaps for shellsort.
0
1, 4, 9, 20, 45, 102, 230, 516, 1158, 2599, 5831, 13082, 29351, 65853, 147748, 331490, 743735, 1668650, 3743800, 8399623, 18845471, 42281871, 94863989, 212837706, 477524607, 1071378536, 2403754591, 5393085583, 12099975682, 27147615084, 60908635199, 136655165852
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
FORMULA
a(n) = ceiling((gamma^n - 1)/(gamma - 1)), where gamma = 2.243609061420001
CROSSREFS
Cf. A108870.
Sequence in context: A020708 A345192 A109110 * A108870 A331942 A111587
KEYWORD
easy,nonn
AUTHOR
Stephen J. Chick, Oct 17 2023
STATUS
approved