A197378 Decimal expansion of least x>0 having sin(x)=(sin(2x/3))^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

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

Table of n, a(n) for n=1..99.

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: A266558 A199869 A378825 * A232738 A201395 A019881

Adjacent sequences: A197375 A197376 A197377 * A197379 A197380 A197381

Keyword

nonn,cons

Author

Clark Kimberling, Oct 14 2011

Status

approved