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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Stephen J. Chick

Stephen J. Chick's wiki page.

Stephen J. Chick has authored 1 sequences.

A366726 Lee's empirically improved Tokuda gaps for shellsort.

Original entry on oeis.org

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

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Author

Stephen J. Chick, Oct 17 2023

Keywords

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

Crossrefs

Cf. A108870.

Formula

a(n) = ceiling((gamma^n - 1)/(gamma - 1)), where gamma = 2.243609061420001

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