A197330 - OEIS

%I #12 Apr 10 2021 11:33:22

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

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

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

%N Decimal expansion of least x > 0 having sin(2*x) = sin(Pi*x/4)^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=1.20938610287170523425443044462680491606...

%t b = 2; c = Pi/4; f[x_] := Sin[x]

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

%t RealDigits[t]  (* A197330 *)

%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