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A197477 Decimal expansion of least x>0 having cos(x)=(cos 3x)^2. 2
8, 4, 1, 8, 3, 5, 5, 3, 5, 6, 1, 4, 3, 6, 3, 8, 0, 7, 4, 8, 5, 7, 3, 2, 6, 7, 6, 5, 6, 2, 1, 6, 4, 3, 0, 7, 6, 5, 3, 5, 8, 5, 7, 8, 5, 5, 3, 3, 9, 3, 6, 3, 3, 0, 6, 4, 3, 9, 5, 3, 0, 8, 4, 2, 8, 3, 1, 2, 0, 2, 8, 3, 2, 1, 4, 7, 6, 8, 9, 1, 4, 5, 1, 4, 8, 3, 3, 7, 8, 4, 4, 7, 7, 7, 4, 5, 5, 5, 9 (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=0.8418355356143638074857326765621643076...

MATHEMATICA

b = 1; c = 3; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, .9}, WorkingPrecision -> 200]

RealDigits[t] (* A197477 *)

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

RealDigits[ ArcCos[ Root[ 1 - 8# - 8#^2 + 16#^3 + 16#^4 &, 2]], 10, 99] // First (* Jean-Fran├žois Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197476.

Sequence in context: A021547 A154527 A145435 * A133839 A080828 A131916

Adjacent sequences:  A197474 A197475 A197476 * A197478 A197479 A197480

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 15 2011

STATUS

approved

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)