A197259 Decimal expansion of least x>0 having sin(2x)=(sin 8x)^2.

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

Offset

-1,1

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=-1..99.

Example

0.0319163652539021088311817322301516...

Mathematica

b = 2; c = 8; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .02, .04}, WorkingPrecision -> 100]
RealDigits[t]  (* A197259*)
Plot[{f[b*x], f[c*x]^2}, {x, 0, .04}]
ArcSin[z]/2 /. FindRoot[16*z^2 - 80*z^4 + 128*z^6 - 64*z^8 - z == 0, {z, 1/30}, WorkingPrecision -> 120] (* Vaclav Kotesovec, Jul 28 2021 *)

Crossrefs

Cf. A197133.

Sequence in context: A317202 A355442 A331732 * A200006 A070894 A090261

Adjacent sequences: A197256 A197257 A197258 * A197260 A197261 A197262

Keyword

nonn,cons

Author

Clark Kimberling, Oct 12 2011

Extensions

Offset and a(99) corrected by Georg Fischer, Jul 28 2021

Status

approved