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%I #12 Jul 28 2021 12:56:31
%S 7,5,0,7,6,2,4,9,0,2,2,7,8,8,1,2,7,5,3,4,1,9,7,3,6,3,1,4,4,3,1,3,9,0,
%T 7,8,5,6,8,2,5,7,2,2,6,5,3,6,1,7,0,5,6,2,8,1,9,2,4,9,7,2,1,3,0,1,6,8,
%U 1,6,8,8,9,7,7,7,2,5,0,4,2,1,4,2,5,2,9,2,5,2,5,6,7,6,8,3,4,1,7
%N Decimal expansion of least x>0 having cos(2*Pi*x)=(cos 2x)^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 0.7507624902278812753419736314431390785682572...
%t b = 2 Pi; c = 2; f[x_] := Cos[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .75, .76}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197519 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%Y Cf. A197476.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 16 2011
%E Offset corrected by _Georg Fischer_, Jul 28 2021
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