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A197260 Decimal expansion of least x>0 having sin(3x)=(sin x)^2. 2
8, 4, 8, 0, 6, 2, 0, 7, 8, 9, 8, 1, 4, 8, 1, 0, 0, 8, 0, 5, 2, 9, 4, 4, 3, 3, 8, 9, 9, 8, 4, 1, 8, 0, 8, 0, 0, 7, 3, 3, 6, 6, 2, 1, 3, 2, 6, 3, 1, 1, 2, 6, 4, 2, 8, 6, 0, 7, 1, 8, 1, 6, 3, 5, 7, 0, 2, 0, 0, 8, 2, 1, 2, 2, 8, 4, 7, 4, 2, 3, 4, 3, 4, 9, 1, 8, 9, 8, 0, 1, 7, 3, 1, 9, 5, 7, 2, 3, 0, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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=0..99.

EXAMPLE

x=0.8480620789814810080529443389984180800...

MATHEMATICA

b = 3; c = 1; f[x_] := Sin[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, 1}, WorkingPrecision -> 100]

RealDigits[t]  (* A197260 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]

RealDigits[ ArcCos[ Sqrt[7]/4], 10, 100] // First (* Jean-Fran├žois Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197133.

Sequence in context: A244210 A019867 A144663 * A155889 A275712 A199266

Adjacent sequences:  A197257 A197258 A197259 * A197261 A197262 A197263

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 12 2011

STATUS

approved

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Last modified December 8 04:31 EST 2019. Contains 329850 sequences. (Running on oeis4.)