A197333 - OEIS

%I #12 Apr 10 2021 11:33:53

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

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

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

%N Decimal expansion of least x > 0 having sin(3*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=0.9016032189481857038023624192861610947620...

%t b = 3; c = Pi/4; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, 1}, WorkingPrecision -> 200]

%t RealDigits[t]  (* A197333 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 13 2011