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%I #12 Sep 08 2021 21:26:03
%S 0,6,5,2,4,6,7,8,0,1,7,9,0,3,0,4,3,3,2,3,4,3,7,0,2,1,7,9,0,8,3,8,2,0,
%T 1,3,8,9,7,9,7,7,5,4,0,8,9,3,3,2,9,5,8,2,5,1,7,2,9,1,8,2,0,8,6,8,0,3,
%U 6,7,7,3,1,2,1,4,1,0,4,6,0,4,5,8,2,0,1
%N Decimal expansion of least x>0 having sin(3x) = 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 x=0.06524678017903043323437021790838201389797754089...
%t b = 3; c = 7; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .05, .2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A197265 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]
%Y Cf. A197133.
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 12 2011
%E a(73) onward corrected by _Sean A. Irvine_, Sep 08 2021
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