|
|
A316389
|
|
Continued fraction expansion of largest root of x^3 - 7*x + 7.
|
|
0
|
|
|
1, 1, 2, 4, 20, 2, 3, 1, 6, 10, 5, 2, 2, 1, 2, 2, 1, 18, 1, 1, 3, 2, 1, 2, 1, 2, 1, 39, 2, 1, 1, 1, 13, 1, 2, 1, 30, 1, 1, 1, 3, 2, 5, 4, 1, 5, 1, 5, 1, 2, 1, 1, 94, 6, 2, 19, 11, 1, 60, 1, 1, 50, 2, 1, 1, 8, 53, 1, 3, 1, 6, 3, 2, 1, 5, 1, 1, 3, 4, 636, 1, 2, 1, 3, 3, 7, 9, 1, 2, 10, 3, 1, 22, 1, 119, 3, 32, 1, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
a(n) is identical to A039921(n-1) for n >= 3. The largest root of x^3 - 7*x + 7 equals (3*w-1)/(2*w-1) for w = 2*cos(Pi/7), where w is the number referenced in A039921. Interestingly enough, all three roots of x^3-7*x+7 have a continued fraction expansion that ends in 2, 3, 1, 6, 10, 5, 2, 2, 1, ... which is a(n) for n >= 5.
|
|
LINKS
|
|
|
EXAMPLE
|
1.69202147163009586962781489700206914019726...
|
|
MATHEMATICA
|
ContinuedFraction[Root[x^3 - 7 x + 7, 3], 100]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,cofr
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|