

A197514


Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/6)^2.


2



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

1,1


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=1..99.


EXAMPLE

x=2.40347697899992522545129646324811831083...


MATHEMATICA

b = 2; c = Pi/6; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.4, 2.41}, WorkingPrecision > 110]
RealDigits[t] (* A197514 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]


CROSSREFS

Cf. A197476.
Sequence in context: A215451 A154585 A020822 * A112635 A222757 A004568
Adjacent sequences: A197511 A197512 A197513 * A197515 A197516 A197517


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 16 2011


STATUS

approved



