

A197508


Decimal expansion of least x > 0 having cos(2*x) = cos(3*Pi*x/2)^2.


2



5, 0, 6, 2, 9, 7, 8, 9, 9, 2, 3, 4, 0, 5, 9, 8, 2, 6, 7, 5, 0, 0, 1, 1, 5, 6, 2, 7, 8, 3, 6, 9, 7, 0, 3, 2, 5, 2, 8, 6, 5, 8, 1, 6, 3, 9, 5, 8, 2, 8, 9, 4, 7, 4, 1, 9, 1, 4, 3, 2, 4, 7, 4, 1, 1, 1, 0, 7, 6, 9, 2, 2, 7, 8, 9, 7, 5, 3, 6, 7, 6, 3, 4, 2, 8, 4, 5
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OFFSET

0,1


COMMENTS

The Mathematica program includes a graph. See A197476 for a guide for the least x > 0 satisfying cos(b*x) = cos(c*x)^2 for selected b and c.


LINKS

Table of n, a(n) for n=0..86.


EXAMPLE

x=0.50629789923405982675001156278369703252865816395828...


MATHEMATICA

b = 2; c = 3 Pi/2; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .5, .51}, WorkingPrecision > 110]
RealDigits[t] (* A197508 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]


CROSSREFS

Cf. A197476.
Sequence in context: A197029 A197030 A035550 * A159751 A190914 A153458
Adjacent sequences: A197505 A197506 A197507 * A197509 A197510 A197511


KEYWORD

nonn,cons,changed


AUTHOR

Clark Kimberling, Oct 15 2011


EXTENSIONS

a(87) onward corrected by Sean A. Irvine, Sep 08 2021


STATUS

approved



