

A197510


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


2



6, 6, 3, 4, 9, 0, 0, 4, 6, 0, 5, 6, 6, 3, 7, 3, 2, 0, 7, 8, 9, 8, 3, 6, 1, 6, 6, 9, 1, 5, 1, 9, 0, 2, 1, 3, 3, 2, 1, 5, 0, 3, 2, 7, 9, 6, 4, 5, 8, 6, 8, 0, 6, 0, 0, 9, 3, 9, 2, 7, 8, 8, 8, 1, 7, 1, 0, 9, 3, 2, 8, 4, 7, 9, 2, 1, 9, 4, 6, 9, 2, 3, 6, 6, 4, 7, 1, 7, 6, 8, 4, 0, 2, 6, 3, 8, 9, 5, 1
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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..98.


EXAMPLE

x=0.66349004605663732078983616691519021...


MATHEMATICA

b = 2; c = Pi; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .7}, WorkingPrecision > 110]
RealDigits[t] (* A197510 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]


CROSSREFS

Cf. A197476.
Sequence in context: A240502 A112112 A193085 * A110632 A202068 A301974
Adjacent sequences: A197507 A197508 A197509 * A197511 A197512 A197513


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 15 2011


STATUS

approved



