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%I #18 Apr 10 2021 11:35:39
%S 5,2,1,3,3,7,8,2,9,5,7,1,7,1,5,6,9,8,6,9,1,9,8,8,5,6,4,4,5,4,9,1,7,9,
%T 7,7,3,0,9,1,8,1,3,9,4,7,3,3,6,8,8,7,1,9,5,4,9,1,8,4,8,6,2,5,1,5,5,9,
%U 0,6,0,9,6,1,0,2,5,9,8,8,8,9,7,4,9,7,5,6,9,0,0,3,9,4,9,7,1,5,1
%N Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(Pi*x/3)^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=0.5213378295717156986919885644549179773091813947336...
%t b = Pi/6; c = Pi/3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197383 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.2}]
%t RealDigits[ (6*ArcSec[ Root[ 16 - 16#^2 + #^6 & , 3]])/Pi, 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y Cf. A197133, A197521.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 14 2011
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