A197135 Decimal expansion of least x>0 having sin(x)=(sin 4x)^2.

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

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

x=0.0638327305078042176623634644603033426...

Mathematica

b = 1; c = 4; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .05, .1}, WorkingPrecision -> 100]
RealDigits[t] (* A197135 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
RealDigits[ ArcCos[ Sqrt[ Root[ 1 - 256#^2 + 2304#^3 - 8192#^4 + 14336#^5 - 12288#^6 + 4096#^7 & , 5]]], 10, 100] // First (* Jean-François Alcover, Feb 19 2013 *)

Crossrefs

Cf. A197133.

Sequence in context: A307110 A307731 A193080 * A365522 A088246 A179559

Adjacent sequences: A197132 A197133 A197134 * A197136 A197137 A197138

Keyword

nonn,cons

Author

Clark Kimberling, Oct 12 2011

Extensions

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

Status

approved