A197255 Decimal expansion of least x>0 having sin(2x)=(sin 4x)^2.

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

Offset

0,2

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=0..107.

Example

0.1364859246184124752043084030419349155...

Mathematica

b = 2; c = 4; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .2}, WorkingPrecision -> 100]
RealDigits[t] (* A197255 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]

Crossrefs

Cf. A197133.

Sequence in context: A197568 A136612 A004546 * A154890 A248176 A100000

Adjacent sequences: A197252 A197253 A197254 * A197256 A197257 A197258

Keyword

nonn,cons

Author

Clark Kimberling, Oct 12 2011

Extensions

a(81) ff. corrected by Georg Fischer, Jul 28 2021

Status

approved