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 A329827 #10 Feb 16 2025 08:33:58
%S A329827 1,3,5,7,9,11,12,14,16,18,20,22,24,25,27,29,31,33,35,36,38,40,42,44,
%T A329827 46,48,49,51,53,55,57,59,60,62,64,66,68,70,72,73,75,77,79,81,83,84,86,
%U A329827 88,90,92,94,96,97,99,101,103,105,107,108,110,112,114,116
%N A329827 Beatty sequence for (5+sqrt(37))/6.
%C A329827 Let r = (5+sqrt(37))/6. Then (floor(n*r)) and (floor(n*r + r/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 A329827 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A329827 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A329827 a(n) = floor(n*r), where r = (5+sqrt(37))/6.
%t A329827 t = 1/3; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
%t A329827 Table[Floor[r*n], {n, 1, 200}] (* A329827 *)
%t A329827 Table[Floor[s*n], {n, 1, 200}] (* A329828 *)
%Y A329827 Cf. A329825, A329828 (complement).
%K A329827 nonn,easy
%O A329827 1,2
%A A329827 _Clark Kimberling_, Dec 31 2019