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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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 15:37 EDT 2021. Contains 347564 sequences. (Running on oeis4.)