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%I #12 Apr 10 2021 13:19:04
%S 1,9,6,0,6,6,9,6,5,4,5,8,7,9,3,5,5,9,3,9,5,4,4,8,6,8,8,3,3,1,5,7,6,5,
%T 6,8,5,3,1,5,9,7,0,0,2,3,6,7,6,8,2,2,3,1,5,7,7,3,5,6,1,5,0,9,2,1,7,0,
%U 1,5,8,8,6,1,8,5,3,3,8,8,4,0,0,3,4,1,5,1,5,3,0,4,5,7,7,5,6,1,9
%N Decimal expansion of least x > 0 having sin(Pi*x/6) = 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=1.9606696545879355939544868833157...
%t b = Pi/6; c = 1; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.95, 1.97},
%t WorkingPrecision -> 200]
%t RealDigits[t] (* A197413 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 1.5, 2.5}]
%Y Cf. A197133.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 14 2011
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