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A197511 Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/2)^2. 2
6, 3, 9, 1, 9, 9, 1, 9, 2, 8, 3, 7, 2, 2, 4, 8, 4, 0, 4, 4, 3, 6, 4, 7, 8, 6, 6, 1, 5, 3, 4, 1, 8, 2, 8, 8, 3, 3, 4, 3, 2, 2, 1, 1, 8, 1, 9, 9, 8, 6, 4, 1, 7, 3, 7, 5, 6, 3, 9, 8, 9, 0, 4, 6, 6, 8, 9, 0, 2, 5, 9, 4, 3, 4, 9, 6, 2, 0, 5, 8, 5, 4, 7, 2, 4, 8, 9, 0, 1, 1, 6, 0, 9, 6, 8, 5, 8, 9, 8 (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..98.

EXAMPLE

x=0.63919919283722484044364786615341828833...

MATHEMATICA

b = 2; c = Pi/2; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .63, .64}, WorkingPrecision -> 110]

RealDigits[t]  (* A197511 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]

CROSSREFS

Cf. A197476.

Sequence in context: A257938 A153632 A308170 * A158606 A021065 A262041

Adjacent sequences:  A197508 A197509 A197510 * A197512 A197513 A197514

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 15 2011

EXTENSIONS

a(98) corrected by Sean A. Irvine, Sep 08 2021

STATUS

approved

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Last modified October 24 10:03 EDT 2021. Contains 348225 sequences. (Running on oeis4.)