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 A329833 #5 Feb 16 2025 08:33:58
%S A329833 1,3,5,6,8,10,11,13,15,16,18,20,22,23,25,27,28,30,32,33,35,37,38,40,
%T A329833 42,44,45,47,49,50,52,54,55,57,59,60,62,64,66,67,69,71,72,74,76,77,79,
%U A329833 81,82,84,86,88,89,91,93,94,96,98,99,101,103,104,106,108
%N A329833 Beatty sequence for (5+sqrt(73))/8.
%C A329833 Let r = (5+sqrt(73))/8. Then (floor(n*r)) and (floor(n*r + 3r/4)) 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 A329833 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A329833 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A329833 a(n) = floor(n*r), where r = (5+sqrt(73))/8.
%t A329833 t = 3/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
%t A329833 Table[Floor[r*n], {n, 1, 200}] (* A329833 *)
%t A329833 Table[Floor[s*n], {n, 1, 200}] (* A329834 *)
%Y A329833 Cf. A329825, A329834 (complement).
%K A329833 nonn,easy
%O A329833 1,2
%A A329833 _Clark Kimberling_, Dec 31 2019