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A197380 Decimal expansion of least x>0 having sin(pi*x/3)=(sin pi*x/6)^2. 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 (list; constant; graph; refs; listen; history; text; internal format)
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=1.7569771238654838925078185040041453453135...

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: A144460 A222541 A177263 * A057785 A305882 A192404

Adjacent sequences:  A197377 A197378 A197379 * A197381 A197382 A197383

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 14 2011

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)