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A197383 Decimal expansion of least x>0 having sin(pi*x/6)=(sin pi*x/3)^2. 3
5, 2, 1, 3, 3, 7, 8, 2, 9, 5, 7, 1, 7, 1, 5, 6, 9, 8, 6, 9, 1, 9, 8, 8, 5, 6, 4, 4, 5, 4, 9, 1, 7, 9, 7, 7, 3, 0, 9, 1, 8, 1, 3, 9, 4, 7, 3, 3, 6, 8, 8, 7, 1, 9, 5, 4, 9, 1, 8, 4, 8, 6, 2, 5, 1, 5, 5, 9, 0, 6, 0, 9, 6, 1, 0, 2, 5, 9, 8, 8, 8, 9, 7, 4, 9, 7, 5, 6, 9, 0, 0, 3, 9, 4, 9, 7, 1, 5, 1 (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..98.

EXAMPLE

x=0.5213378295717156986919885644549179773091813947336...

MATHEMATICA

b = Pi/6; c = Pi/3; f[x_] := Sin[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 200]

RealDigits[t] (* A197383 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.2}]

RealDigits[ (6*ArcSec[ Root[ 16 - 16#^2 + #^6 & , 3]])/Pi, 10, 99] // First (* Jean-Fran├žois Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197133, A197521.

Sequence in context: A158625 A133615 A136161 * A266455 A091505 A030357

Adjacent sequences:  A197380 A197381 A197382 * A197384 A197385 A197386

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 14 2011

STATUS

approved

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Last modified January 21 19:39 EST 2019. Contains 319350 sequences. (Running on oeis4.)