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 A330002 #17 Jun 20 2025 00:22:34
%S A330002 1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,
%T A330002 32,33,34,36,37,38,39,41,42,43,44,46,47,48,49,51,52,53,54,56,57,58,59,
%U A330002 61,62,63,64,66,67,68,69,71,72,73,74,76,77,78,79,81,82,83
%N A330002 Beatty sequence for x, where 1/x + 1/(x+1)^2 = 1.
%C A330002 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.
%C A330002 Differs from A047201 first at A047201(85)=106, a(85)=105. - _R. J. Mathar_, Jan 11 2020
%H A330002 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence.</a>
%H A330002 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F A330002 a(n) = floor(n*x), where x = 1.24697960371... is the constant in A255249.
%p A330002 A330002 := proc(n)
%p A330002 local x;
%p A330002 x := -2*cos(5*Pi/7) ;
%p A330002 floor(n*x) ;
%p A330002 end proc: # _R. J. Mathar_, Jan 11 2020
%t A330002 r = x /. FindRoot[1/x + 1/(x+1)^2 == 1, {x, 2, 10}, WorkingPrecision -> 120]
%t A330002 RealDigits[r][[1]] (* A255249 *)
%t A330002 Table[Floor[n*r], {n, 1, 250}] (* A330002 *)
%t A330002 Table[Floor[n*(1+r)^2], {n, 1, 250}] (* A330003 *)
%Y A330002 Cf. A329825, A255249, A330003 (complement).
%K A330002 nonn,easy
%O A330002 1,2
%A A330002 _Clark Kimberling_, Jan 04 2020