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.
%I A329829 #5 Feb 16 2025 08:33:58
%S A329829 1,3,5,6,8,10,12,13,15,17,18,20,22,24,25,27,29,30,32,34,36,37,39,41,
%T A329829 43,44,46,48,49,51,53,55,56,58,60,61,63,65,67,68,70,72,73,75,77,79,80,
%U A329829 82,84,86,87,89,91,92,94,96,98,99,101,103,104,106,108,110
%N A329829 Beatty sequence for (2+sqrt(10))/3.
%C A329829 Let r = (2+sqrt(10))/3. Then (floor(n*r)) and (floor(n*r + 2r/3)) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.
%H A329829 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A329829 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A329829 a(n) = floor(n*r), where r = (2+sqrt(10))/3.
%t A329829 t = 2/3; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
%t A329829 Table[Floor[r*n], {n, 1, 200}] (* A329829 *)
%t A329829 Table[Floor[s*n], {n, 1, 200}] (* A329830 *)
%Y A329829 Cf. A329825, A329830 (complement).
%K A329829 nonn,easy
%O A329829 1,2
%A A329829 _Clark Kimberling_, Dec 31 2019