|
|
A197758
|
|
Decimal expansion of least x>0 having sin(2x)=4*sin(8x).
|
|
5
|
|
|
3, 7, 1, 4, 5, 8, 2, 9, 4, 0, 3, 3, 4, 8, 6, 3, 5, 2, 5, 0, 5, 8, 3, 2, 7, 2, 8, 5, 1, 9, 5, 1, 2, 4, 0, 9, 8, 0, 8, 9, 6, 8, 2, 6, 0, 7, 3, 9, 5, 7, 5, 3, 9, 0, 7, 2, 3, 4, 4, 5, 2, 9, 1, 0, 6, 3, 6, 6, 8, 0, 5, 8, 1, 2, 0, 6, 6, 9, 3, 6, 8, 8, 6, 9, 9, 1, 5, 1, 0, 5, 8, 9, 8, 3, 6, 8, 1, 2, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
For a discussion and guide to related sequences, see A197739.
|
|
LINKS
|
|
|
EXAMPLE
|
x=0.37145829403348635250583272851951240980...
|
|
MATHEMATICA
|
b = 1; c = 4;
f[x_] := Cos[b*x]^2; g[x_] := Sin[c*x]^2; s[x_] := f[x] + g[x];
r = x /. FindRoot[b*Sin[2 b*x] == c*Sin[2 c*x], {x, .37, .38}, WorkingPrecision -> 110]
m = s[r]
Plot[{b*Sin[2 b*x], c*Sin[2 c*x]}, {x, 0, Pi}]
d = m/2; t = x /. FindRoot[s[x] == d, {x, 0.64, 0.65}, WorkingPrecision -> 110]
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = m/3; t = x /. FindRoot[s[x] == d, {x, 0.72, 0.73}, WorkingPrecision -> 110]
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = 1; t = x /. FindRoot[s[x] == d, {x, 0.6, 0.7}, WorkingPrecision -> 110]
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = 1/2; t = x /. FindRoot[s[x] == d, {x, 0.6, 0.8}, WorkingPrecision -> 110]
Plot[{s[x], d}, {x, 0, 1}, AxesOrigin -> {0, 0}]
RealDigits[ ArcTan[ Sqrt[ Root[17#^3 - 109#^2 + 115# - 15&, 1] ] ], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|