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%I #15 Apr 10 2021 11:35:00
%S 8,8,7,3,6,0,4,8,4,4,7,7,8,5,1,6,3,6,8,6,1,3,1,4,2,5,6,8,0,8,3,6,9,0,
%T 1,2,5,1,3,0,6,8,4,3,9,8,9,4,4,2,1,2,8,2,1,5,5,7,2,9,6,2,2,6,0,6,1,9,
%U 8,2,8,8,7,9,9,0,9,8,9,9,9,6,4,7,5,8,9,9,9,1,8,3,6,4,8,4,8,3,8
%N Decimal expansion of least x > 0 having sin(Pi*x/4) = 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=0.88736048447785163686131425680836901251306...
%t b = Pi/4; c = Pi/3; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.8, 1}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197381 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]
%t (* or *)
%t RealDigits[12*ArcTan[Sqrt[Root[9 - 217*#1 + 1085*#1^2 - 1501*#1^3 + 1019*#1^4 - 267*#1^5 - #1^6 + #1^7 & , 2]]]/Pi, 10, 120][[1]] (* _Vaclav Kotesovec_, Nov 14 2015 *)
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 14 2011
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