A197261 - OEIS

%I #14 Sep 16 2021 03:21:47

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

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

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

%N Decimal expansion of least x>0 having sin(3x) = sin(2x)^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.

%F Equals arcsin((1+4*cos((Pi+arccos(37/64))/3))/3). - _Gleb Koloskov_, Sep 15 2021

%e 0.650240618217618192095555172734670514...

%t b = 3; c = 2; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .5, .7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197261 *)

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

%o (PARI) asin((1+4*cos((Pi+acos(37/64))/3))/3) \\ _Gleb Koloskov_, Sep 15 2021

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 12 2011