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%I #8 Feb 19 2013 06:23:45
%S 8,4,1,8,3,5,5,3,5,6,1,4,3,6,3,8,0,7,4,8,5,7,3,2,6,7,6,5,6,2,1,6,4,3,
%T 0,7,6,5,3,5,8,5,7,8,5,5,3,3,9,3,6,3,3,0,6,4,3,9,5,3,0,8,4,2,8,3,1,2,
%U 0,2,8,3,2,1,4,7,6,8,9,1,4,5,1,4,8,3,3,7,8,4,4,7,7,7,4,5,5,5,9
%N Decimal expansion of least x>0 having cos(x)=(cos 3x)^2.
%C The Mathematica program includes a graph. See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.
%e x=0.8418355356143638074857326765621643076...
%t b = 1; c = 3; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, .9}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197477 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%t RealDigits[ ArcCos[ Root[ 1 - 8# - 8#^2 + 16#^3 + 16#^4 &, 2]], 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 15 2011
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