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 A329832 #5 Feb 16 2025 08:33:58
%S A329832 2,4,6,8,10,12,14,17,19,21,23,25,27,29,31,34,36,38,40,42,44,46,49,51,
%T A329832 53,55,57,59,61,63,66,68,70,72,74,76,78,81,83,85,87,89,91,93,95,98,
%U A329832 100,102,104,106,108,110,113,115,117,119,121,123,125,127,130,132
%N A329832 Beatty sequence for (9+sqrt(65))/8.
%C A329832 Let r = (7+sqrt(65))/8. Then (floor(n*r)) and (floor(n*r + r/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 A329832 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A329832 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A329832 a(n) = floor(n*s), where s = (9+sqrt(65))/8.
%t A329832 t = 1/4; r = Simplify[(2 - t + Sqrt[t^2 + 4])/2]; s = Simplify[r/(r - 1)];
%t A329832 Table[Floor[r*n], {n, 1, 200}] (* A329831 *)
%t A329832 Table[Floor[s*n], {n, 1, 200}] (* A329832 *)
%Y A329832 Cf. A329825, A329831 (complement).
%K A329832 nonn,easy
%O A329832 1,1
%A A329832 _Clark Kimberling_, Dec 31 2019