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 A374723 #55 Sep 05 2024 03:29:09
%S A374723 1,4,120,74455920,479301523749226879680,
%T A374723 1336367227479573478314645756081634359006026455038720
%N A374723 Numerator of rational number tan(2^(n-1)*arctan(1/A024810(n))).
%C A374723 r(n) = tan(2^(n-1)*arctan(1/A024810(n))) is always a rational number such that its limit lim_{n->oo} r(n)=1.
%H A374723 Sanjar M. Abrarov, Rajinder K. Jagpal, Rehan Siddiqui, and Brendan M. Quine, <a href="https://doi.org/10.3390/mca29020017">An Iterative Method for Computing π by Argument Reduction of the Tangent Function</a>, Math. Comput. Appl. 2024, 29(2), 17.
%F A374723 a(n) = numerator(tan(2^(n-1)*arctan(1/A024810(n)))).
%t A374723 a[0] := 0;
%t A374723 a[n_] := Sqrt[2 + a[n - 1]];
%t A374723 b[n_] := Floor[a[n]/Sqrt[2 - a[n - 1]]];
%t A374723 r[0, x_] := 1;
%t A374723 r[1, x_] := (2*x)/(1 - x^2);
%t A374723 r[n_, x_] := (2*r[n - 1, x])/(1 - r[n - 1, x]^2);
%t A374723 k = 1;
%t A374723 While[k <= 6, Print[k, " ", Numerator[r[k - 1, 1/b[k]]]]; k++];
%Y A374723 Cf. A024810, A375935 (denominators).
%K A374723 nonn,frac
%O A374723 1,2
%A A374723 _Sanjar Abrarov_, Sep 03 2024