A197290 - OEIS

%I #10 Aug 11 2021 15:30:27

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

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

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

%N Decimal expansion of least x>0 having sin(6x)=(sin x)^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=0.4868248820126508954044126405332359296...

%t b = 6; c = 1; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197290 *)

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

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 13 2011

%E Offset corrected by _Georg Fischer_, Aug 10 2021