A197331 - OEIS

%I #13 Apr 10 2021 09:18:06

%S 1,3,5,2,4,0,4,8,2,8,4,2,2,2,7,8,5,5,5,7,0,3,5,4,3,6,2,8,9,2,9,2,4,1,

%T 6,4,2,1,4,3,0,6,4,6,0,3,1,1,5,6,1,9,0,4,1,5,8,8,7,0,2,1,4,5,4,9,9,4,

%U 1,9,1,1,3,0,5,5,7,7,5,8,2,7,6,5,6,1,1,8,0,0,5,0,8,3,6,7,6,7,7

%N Decimal expansion of least x > 0 having sin(2*x) = sin(Pi*x/6)^2.

%C The Mathematica program includes a graph. See A197133 for a guide to least x > 0 satisfying sin(b*x) = sin(c*x)^2 for selected b and c.

%e x=1.35240482842227855570354362892924164214...

%t b = 2; c = Pi/6; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1, 1.5}, WorkingPrecision -> 200]

%t RealDigits[t]  (* A197331 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.5}]

%Y Cf. A197133.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 13 2011