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%I #12 Jul 28 2021 06:37:20
%S 0,2,8,0,3,7,6,3,0,0,4,5,4,9,8,0,0,3,2,3,3,1,3,5,4,8,0,4,0,4,7,2,2,1,
%T 8,2,5,3,4,4,9,2,9,2,1,5,5,4,5,5,9,3,5,1,8,6,3,3,6,0,7,3,3,8,5,5,8,9,
%U 6,1,8,6,8,0,0,5,6,7,8,4,8,3,2,1,9,5,3,7,3,5,8,9,2,9,0,1,6,9,7,4,0
%N Decimal expansion of least x>0 having sin(x)=(sin 6x)^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.
%t x=0.028037630045498003233135480404722182534...
%t b = 1; c = 6; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .01, .1}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197252 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 12 2011
%E Offset corrected by _Georg Fischer_, Jul 28 2021
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