A197269 Decimal expansion of least x>0 having sin(4x)=(sin 5x)^2.

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

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..99.

Example

x=0.34256647627752224363603774577088571163...

Mathematica

b = 4; c = 5; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .5}, WorkingPrecision -> 100]
RealDigits[t] (* A197269 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]

Crossrefs

Cf. A197133.

Sequence in context: A117041 A209688 A143939 * A201905 A138609 A322466

Adjacent sequences: A197266 A197267 A197268 * A197270 A197271 A197272

Keyword

nonn,cons

Author

Clark Kimberling, Oct 12 2011

Status

approved