|
|
A093053
|
|
Continued fraction expansion of a constant x such that the n-th partial quotient equals a(n) = floor(2^n*x), with a(0)=1.
|
|
1
|
|
|
1, 2, 5, 11, 23, 46, 93, 186, 372, 745, 1490, 2980, 5960, 11921, 23843, 47686, 95373, 190746, 381493, 762986, 1525973, 3051946, 6103893, 12207787, 24415575, 48831150, 97662301, 195324602, 390649204, 781298409, 1562596819, 3125193638
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Decimal expansion is given by A093054. The partial quotients of the continued fraction expansion of 2^m*x include many similar terms. For example, the continued fraction of 2*x is given by: [2;1,10,5,1,1,11,92,46,1,1,92,1,1,185,1,1,372,2980,1490,11920,5960,1,1,11921,95372,47686,1,1,95372,1,1,...].
|
|
LINKS
|
|
|
EXAMPLE
|
x=[1;2,5,11,23,46,93,186,372,745,1490,2980,5960,11921,23843,...].
x=1.455281692832971051393034444524589699271213777825554774132070945742167...
|
|
MAPLE
|
{L=500; x=sqrt(2); for(i=1, 10, cf=vector(L, n, floor(x*2^(n-1))); cm=contfracpnqn(cf); x=cm[1, 1]/cm[2, 1])}
|
|
CROSSREFS
|
|
|
KEYWORD
|
cofr,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|