A197375 Decimal expansion of least x > 0 having sin(3*x) = sin(Pi*x/6)^2.

9, 6, 7, 9, 1, 9, 9, 1, 7, 1, 6, 2, 8, 4, 0, 1, 2, 4, 6, 1, 0, 7, 0, 3, 7, 5, 3, 8, 3, 1, 8, 3, 0, 1, 7, 4, 1, 3, 5, 2, 2, 3, 3, 0, 3, 9, 8, 2, 9, 3, 4, 7, 6, 7, 0, 1, 7, 9, 1, 5, 6, 8, 1, 4, 0, 9, 1, 6, 1, 9, 1, 7, 8, 8, 2, 1, 0, 4, 5, 9, 5, 3, 9, 4, 9, 3, 7, 5, 7, 7, 2, 1, 1, 6, 6, 9, 3, 1, 0

Offset

0,1

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=0..98.

Example

x=0.967919917162840124610703753831830174...

Mathematica

b = 3; c = Pi/6; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, 1}, WorkingPrecision -> 200]
RealDigits[t] (*  *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]

Crossrefs

Cf. A197133.

Sequence in context: A340577 A229923 A203080 * A019643 A011012 A157989

Adjacent sequences: A197372 A197373 A197374 * A197376 A197377 A197378

Keyword

nonn,cons

Author

Clark Kimberling, Oct 14 2011

Status

approved