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 A330003 #15 Jun 20 2025 00:22:47
%S A330003 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,106,111,
%T A330003 116,121,126,131,136,141,146,151,156,161,166,171,176,181,186,191,196,
%U A330003 201,207,212,217,222,227,232,237,242,247,252,257,262,267,272,277,282
%N A330003 Beatty sequence for (x+1)^2, where 1/x + 1/(x+1)^2 = 1.
%C A330003 Let x be the solution of 1/x + 1/(x+1)^2 = 1. Then (floor(n x) and (floor(n (x+1)^2))) 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 A330003 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A330003 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A330003 a(n) = floor(n x), where x = 1.24697960371... is the constant in A255249.
%t A330003 r = x /. FindRoot[1/x + 1/(x+1)^2 == 1, {x, 2, 10}, WorkingPrecision -> 120]
%t A330003 RealDigits[r][[1]] (* A255249 *)
%t A330003 Table[Floor[n*r], {n, 1, 250}] (* A330002 *)
%t A330003 Table[Floor[n*(1+r)^2], {n, 1, 250}] (* A330003 *)
%Y A330003 Cf. A329825, A255249, A330002 (complement).
%K A330003 nonn,easy
%O A330003 1,1
%A A330003 _Clark Kimberling_, Jan 04 2020