|
|
A197490
|
|
Decimal expansion of least x > 0 having cos(x) = cos(2*Pi*x)^2.
|
|
2
|
|
|
5, 6, 4, 4, 2, 5, 4, 7, 6, 0, 6, 2, 6, 5, 9, 0, 9, 9, 3, 8, 4, 0, 0, 3, 2, 2, 8, 9, 3, 7, 7, 8, 8, 2, 9, 7, 6, 7, 7, 4, 9, 8, 5, 5, 2, 8, 2, 2, 8, 6, 1, 8, 0, 6, 1, 3, 5, 9, 1, 0, 5, 4, 9, 2, 1, 7, 4, 1, 1, 0, 3, 1, 7, 3, 3, 4, 6, 2, 5, 7, 9, 7, 5, 7, 0, 3, 5, 6, 1, 7, 0, 5, 0, 5, 5, 0, 4, 2, 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
|
|
|
EXAMPLE
|
x=0.564425476062659099384003228937788297677...
|
|
MATHEMATICA
|
b = 1; c = 2 Pi; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .56, .57}, WorkingPrecision -> 110]
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|