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%I #12 Apr 10 2021 13:18:47
%S 3,2,8,1,3,7,2,2,9,5,3,1,1,0,4,9,8,9,9,4,2,4,7,9,8,3,5,4,8,3,9,6,1,9,
%T 2,2,0,2,2,6,2,0,6,6,2,9,3,8,6,2,2,6,7,8,2,6,3,8,5,7,0,6,9,2,5,6,4,6,
%U 8,4,3,8,5,9,1,0,5,5,0,5,4,3,1,2,1,6,5,0,7,0,0,5,7,5,8,2,0,4,2
%N Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(x/4)^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=3.281372295311049899424798354839619220...
%t b = Pi/4; c = 1/4; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3.2, 3.5}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197412 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2*Pi}]
%Y Cf. A197133.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 14 2011
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