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%I #9 Apr 10 2021 23:59:48
%S 3,9,3,6,9,6,4,2,4,7,6,1,2,8,3,7,4,1,8,8,3,3,5,3,0,4,7,0,0,9,7,7,6,6,
%T 0,0,4,3,8,5,1,3,2,5,9,6,8,3,3,0,3,9,9,7,6,6,8,4,1,5,4,8,2,1,1,0,7,2,
%U 5,1,2,5,2,0,4,9,3,6,9,8,0,5,0,0,0,3,6,5,7,8,2,8,9,6,5,9,3,5,0
%N Decimal expansion of least x > 0 having cos(x) = cos(2*Pi*x)^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=0.3936964247612837418833530470097766004385132...
%t b = 1; c = 2*Pi; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .39, .4}, WorkingPrecision -> 200]
%t RealDigits[t] (* A197572 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, .5}]
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 16 2011
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