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%I #19 Jul 28 2021 07:21:56
%S 2,1,1,4,4,9,8,2,9,4,0,9,7,4,0,0,3,5,4,9,4,7,5,9,3,5,4,2,6,5,1,5,5,6,
%T 8,4,4,2,9,3,1,9,2,8,5,6,6,7,8,4,9,2,6,3,2,4,0,0,4,6,6,1,2,2,8,2,3,7,
%U 3,1,1,3,9,2,8,3,8,4,1,9,7,9,6,0,9,7,1,4,2,0,6,3,1,3,2,6,1,1,7
%N Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(Pi*x/6)^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=2.1144982940974003549475935426515568442931... [corrected by _Georg Fischer_, Jul 28 2021]
%t b = Pi/3; c = Pi/6; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197380 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]
%t RealDigits[ 6*ArcCos[1/Sqrt[5]]/Pi, 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y Cf. A197133.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 14 2011
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