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 A197383 Decimal expansion of least x>0 having sin(pi*x/6)=(sin pi*x/3)^2. 3

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of least x>0 having sin(pi*x/6)=(sin pi*x/3)^2.

%C 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.

%e x=0.5213378295717156986919885644549179773091813947336...

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

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

%t RealDigits[t] (* A197383 *)

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

%t RealDigits[ (6*ArcSec[ Root[ 16 - 16#^2 + #^6 & , 3]])/Pi, 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)

%Y Cf. A197133, A197521.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 14 2011

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)