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%I #12 Aug 04 2018 04:12:36
%S 2,0,5,4,8,0,4,2,1,7,1,7,7,4,3,1,8,7,0,3,5,4,1,8,4,5,3,8,4,5,8,4,8,0,
%T 0,4,4,1,0,6,7,0,2,5,7,5,2,5,4,4,4,1,2,1,3,4,8,7,1,8,9,6,7,4,2,9,1,0,
%U 3,1,2,3,5,6,2,4,4,0,2,2,3,5,8,2,1,1,7,0,4,5,6,7,9,1,4,5,3,6,3,7
%N Decimal expansion of least x>0 having sin x = (sin 7x)^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 0.0205480421717743187035418453845848004410...
%t b = 1; c = 7; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .01, .1}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197253 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%o (PARI) solve(x=.01,.03,sin(x)-sin(7*x)^2) \\ _Charles R Greathouse IV_, Dec 28 2011
%Y Cf. A197133.
%K nonn,cons
%O -1,1
%A _Clark Kimberling_, Oct 12 2011