A197380 Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(Pi*x/6)^2.

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

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=2.1144982940974003549475935426515568442931... [corrected by Georg Fischer, Jul 28 2021]

Mathematica

b = Pi/3; c = Pi/6; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]
RealDigits[t] (* A197380 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]
RealDigits[ 6*ArcCos[1/Sqrt[5]]/Pi, 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)

Crossrefs

Cf. A197133.

Sequence in context: A222541 A177263 A357050 * A057785 A305882 A339285

Adjacent sequences: A197377 A197378 A197379 * A197381 A197382 A197383

Keyword

nonn,cons

Author

Clark Kimberling, Oct 14 2011

Status

approved