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 A197378 Decimal expansion of least x>0 having sin(x)=(sin(2x/3))^2. 2
 1, 9, 5, 0, 7, 2, 1, 8, 5, 4, 6, 5, 2, 8, 5, 4, 5, 7, 6, 2, 8, 6, 6, 6, 5, 5, 1, 8, 2, 0, 4, 0, 1, 1, 5, 4, 4, 6, 4, 5, 0, 1, 6, 3, 4, 2, 9, 2, 8, 2, 1, 8, 2, 3, 0, 8, 4, 5, 4, 6, 0, 2, 4, 3, 6, 0, 3, 5, 8, 9, 9, 8, 7, 1, 5, 7, 0, 7, 0, 3, 3, 2, 5, 1, 5, 5, 4, 0, 3, 5, 5, 1, 6, 0, 0, 0, 4, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE x=1.9507218546528545762866655182040115446450... MATHEMATICA b = 1; c = 2/3; f[x_] := Sin[x] t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200] RealDigits[t] (* A197378 *) Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}] RealDigits[ 3*ArcCos[Root[1 - 8 #^2 + 16 #^6 &, 4]], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *) CROSSREFS Cf. A197133. Sequence in context: A145436 A199509 A199869 * A201395 A019881 A049256 Adjacent sequences:  A197375 A197376 A197377 * A197379 A197380 A197381 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 14 2011 STATUS approved

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