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A197377 Decimal expansion of least x>0 having sin(x)=(sin(x/3))^2. 2
2, 5, 4, 4, 1, 8, 6, 2, 3, 6, 9, 4, 4, 4, 4, 3, 0, 2, 4, 1, 5, 8, 8, 3, 3, 0, 1, 6, 9, 9, 5, 2, 5, 4, 2, 4, 0, 2, 2, 0, 0, 9, 8, 6, 3, 9, 7, 8, 9, 3, 3, 7, 9, 2, 8, 5, 8, 2, 1, 5, 4, 4, 9, 0, 7, 1, 0, 6, 0, 2, 4, 6, 3, 6, 8, 5, 4, 2, 2, 7, 0, 3, 0, 4, 7, 5, 6, 9, 4, 0, 5, 1, 9, 5, 8, 7, 1, 6, 9 (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=2.54418623694444302415883301699525424022009...

MATHEMATICA

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

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.3, 2.6}, WorkingPrecision -> 200]

RealDigits[t] (* A197377 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.7}]

RealDigits[ 3*ArcCos[Sqrt[7]/4], 10, 99] // First (* Jean-Fran├žois Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197133.

Sequence in context: A266416 A266401 A083798 * A172483 A211247 A021397

Adjacent sequences:  A197374 A197375 A197376 * A197378 A197379 A197380

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 14 2011

STATUS

approved

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Last modified August 3 06:43 EDT 2021. Contains 346435 sequences. (Running on oeis4.)