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 A197833 #8 Apr 10 2021 22:31:12
%S A197833 1,6,4,8,4,3,9,4,6,7,0,4,9,4,0,0,1,2,6,0,0,5,7,0,3,5,6,1,9,0,8,8,9,8,
%T A197833 8,9,3,0,5,2,3,2,1,8,4,8,0,9,1,2,4,0,2,0,0,3,4,0,6,2,7,1,5,7,2,6,6,6,
%U A197833 6,8,0,3,5,6,2,9,5,3,6,9,4,7,4,3,7,0,6,5,7,8,5,2,5,2,9,6,4,1,3
%N A197833 Decimal expansion of least x > 0 having sin(2*x) = 3*Pi*sin(3*Pi*x).
%C A197833 For a discussion and guide to related sequences, see A197739.
%e A197833 x=0.16484394670494001260057035619088988930523218...
%t A197833 b = 1; c = 3*Pi;
%t A197833 f[x_] := Cos[b*x]^2; g[x_] := Sin[c*x]^2; s[x_] := f[x] + g[x];
%t A197833 r = x /. FindRoot[b*Sin[2 b*x] == c*Sin[2 c*x], {x, .16, .17}, WorkingPrecision -> 110]
%t A197833 RealDigits[r](* A197833 *)
%t A197833 m = s[r]
%t A197833 RealDigits[m](* A197834 *)
%t A197833 Plot[{b*Sin[2 b*x], c*Sin[2 c*x]}, {x, 0, .6}]
%t A197833 d = m/2; t = x /. FindRoot[s[x] == d, {x, .4, .42}, WorkingPrecision -> 110]
%t A197833 RealDigits[t] (* A197835 *)
%t A197833 Plot[{s[x], d}, {x, 0, .7}, AxesOrigin -> {0, 0}]
%t A197833 d = m/3; t = x /. FindRoot[s[x] == d, {x, .91, .92}, WorkingPrecision -> 110]
%t A197833 RealDigits[t](* A197836 *)
%t A197833 Plot[{s[x], d}, {x, 0, Pi/2}, AxesOrigin -> {0, 0}]
%t A197833 d = 1; t = x /. FindRoot[s[x] == d, {x, .4, .5}, WorkingPrecision -> 110]
%t A197833 RealDigits[t] (* A197837 *)
%t A197833 Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
%t A197833 d = 1/2; t = x /. FindRoot[s[x] == d, {x, .95, .96}, WorkingPrecision -> 110]
%t A197833 RealDigits[t] (* A197838 *)
%t A197833 Plot[{s[x], d}, {x, 0, 1}, AxesOrigin -> {0, 0}]
%Y A197833 Cf. A197739.
%K A197833 nonn,cons
%O A197833 0,2
%A A197833 _Clark Kimberling_, Oct 19 2011