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 A330118 #9 Feb 16 2025 08:33:59
%S A330118 2,4,6,9,11,13,16,18,20,23,25,27,30,32,34,37,39,41,44,46,48,51,53,55,
%T A330118 58,60,62,65,67,69,72,74,76,79,81,83,86,88,90,92,95,97,99,102,104,106,
%U A330118 109,111,113,116,118,120,123,125,127,130,132,134,137,139,141
%N A330118 Beatty sequence for 1+x+x^2, where 1/(1+x) + 1/(1+x+x^2) = 1.
%C A330118 Let x be the positive solution of 1/(1+x) + 1/(1+x+x^2) = 1. Then (floor(n*(1+x))) and (floor(n*(1+x+x^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 A330118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A330118 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A330118 a(n) = floor(n*(1+x+x^2)), where x = 0.7548776662... is the constant in A075778.
%t A330118 r = x /. FindRoot[1/(1 + x) + 1/(1 + x + x^2) == 1, {x, 1, 2}, WorkingPrecision -> 200]
%t A330118 RealDigits[r] (* A075778 *)
%t A330118 Table[Floor[n*(1 + r)], {n, 1, 250}] (* A330117 *)
%t A330118 Table[Floor[n*(1 + r + r^2)], {n, 1, 250}] (* A330118 *)
%t A330118 Plot[1/(1 + x) + 1/(1 + x + x^2) - 1, {x, 0, 2}]
%Y A330118 Cf. A329825, A075778, A330117 (complement).
%K A330118 nonn,easy
%O A330118 1,1
%A A330118 _Clark Kimberling_, Jan 04 2020