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%I #16 Jul 28 2021 11:50:45
%S 3,1,9,1,6,3,6,5,2,5,3,9,0,2,1,0,8,8,3,1,1,8,1,7,3,2,2,3,0,1,5,1,6,7,
%T 1,3,0,5,9,0,8,5,5,6,0,6,7,2,2,3,0,1,5,0,2,7,0,8,6,9,1,3,1,3,2,9,5,4,
%U 8,0,5,7,1,3,6,7,6,2,4,6,4,5,7,0,4,1,5,0,2,1,1,0,2,4,0,2,2,4,2,6,9
%N Decimal expansion of least x>0 having sin(2x)=(sin 8x)^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 0.0319163652539021088311817322301516...
%t b = 2; c = 8; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .02, .04}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197259*)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, .04}]
%t ArcSin[z]/2 /. FindRoot[16*z^2 - 80*z^4 + 128*z^6 - 64*z^8 - z == 0, {z, 1/30}, WorkingPrecision -> 120] (* _Vaclav Kotesovec_, Jul 28 2021 *)
%Y Cf. A197133.
%K nonn,cons
%O -1,1
%A _Clark Kimberling_, Oct 12 2011
%E Offset and a(99) corrected by _Georg Fischer_, Jul 28 2021
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