|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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]
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|