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 A024810 #54 Jul 08 2024 23:43:25
%S A024810 1,2,5,10,20,40,81,162,325,651,1303,2607,5215,10430,20860,41721,83443,
%T A024810 166886,333772,667544,1335088,2670176,5340353,10680707,21361414,
%U A024810 42722829,85445659,170891318,341782637,683565275,1367130551,2734261102,5468522204,10937044409
%N A024810 a(n) = floor( tan(m*Pi/2) ), where m = 1 - 2^(-n).
%C A024810 Geometrically, each term of the sequence represents the integer part of the distance between opposite vertices and also edges of even sided polygons, each of which has double the number of sides of the previous, starting with a square of unit length. - _Torlach Rush_, Feb 21 2014
%C A024810 a(n) is the greatest integer k such that k/2^n < 2/Pi. - _Clark Kimberling_, Oct 10 2017
%C A024810 Number of roots of sin(1/x) = 0 in interval 1/2^(n+1) < x < 1. - _Hugo Pfoertner_, Oct 24 2019
%C A024810 Or simply: number of zeros of sin(x) in the range [1, 2^(n+1)]. - _M. F. Hasler_, Oct 25 2019
%H A024810 Vincenzo Librandi, <a href="/A024810/b024810.txt">Table of n, a(n) for n = 1..1000</a>
%H A024810 Sanjar M. Abrarov, Rajinder K. Jagpal, Rehan Siddiqui, and Brendan M. Quine, <a href="https://arxiv.org/abs/2107.01027">Algorithmic determination of a large integer in the two-term Machin-like formula for pi</a>, arXiv:2107.01027 [math.GM], 2021.
%H A024810 Hugo Pfoertner, <a href="/A024810/a024810.pdf">Illustration of initial terms</a>, sin(1/x) plotted on logarithmic x axis.
%F A024810 a(n) = floor( 1 / tan( Pi / 2^(n+1) )). - _Michael Somos_, Feb 24 2014
%F A024810 a(n) = floor(2^(n+1)/Pi). - _Clark Kimberling_, Oct 10 2017 [Corrected by _Michel Marcus_, Oct 25 2019]
%F A024810 From _Sanjar Abrarov_, Jun 20 2024: (Start)
%F A024810 a(n) = floor(c_n/sqrt(2-c_{n-1})), where c_n=sqrt(2+c_{n-1}) and c_0 = 0.
%F A024810 a(n) = 2*a(n-1)+A127266(n). (End)
%t A024810 Table[Floor[Tan[(1 - 2^(-n)) Pi/2]], {n, 1, 40}] (* _Vincenzo Librandi_, Feb 26 2014 *)
%o A024810 (PARI) a(n) = floor(tan((1 - 2^(-n))*Pi/2)) \\ _Michel Marcus_, Mar 23 2013
%o A024810 (PARI) A024810(n)=2^(n+1)\Pi \\ _M. F. Hasler_, Oct 25 2019
%Y A024810 Cf. A127266 (mod 2), A172265 (partial sums).
%K A024810 nonn
%O A024810 1,2
%A A024810 _Clark Kimberling_
%E A024810 a(30)-a(33) corrected by _Michel Marcus_, Mar 23 2013