cp's OEIS Frontend

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.

A366726 Lee's empirically improved Tokuda gaps for shellsort.

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%I A366726 #26 Jan 22 2024 05:42:34
%S A366726 1,4,9,20,45,102,230,516,1158,2599,5831,13082,29351,65853,147748,
%T A366726 331490,743735,1668650,3743800,8399623,18845471,42281871,94863989,
%U A366726 212837706,477524607,1071378536,2403754591,5393085583,12099975682,27147615084,60908635199,136655165852
%N A366726 Lee's empirically improved Tokuda gaps for shellsort.
%C A366726 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.
%C A366726 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...
%H A366726 Ying Wai Lee, <a href="https://arxiv.org/abs/2112.11112">Empirically Improved Tokuda Gap Sequence in Shellsort</a>, arXiv:2112.11112 [cs.DS], 2021.
%F A366726 a(n) = ceiling((gamma^n - 1)/(gamma - 1)), where gamma = 2.243609061420001
%Y A366726 Cf. A108870.
%K A366726 easy,nonn
%O A366726 1,2
%A A366726 _Stephen J. Chick_, Oct 17 2023