|
|
A085395
|
|
Denominators of convergents to the Thue-Morse constant 0.41245403364...
|
|
4
|
|
|
1, 2, 5, 12, 17, 80, 257, 1365, 2987, 4352, 20395, 45142, 65537, 372827, 16469925, 16842752, 83840933, 100683685, 285208303, 1241516897, 1526725200, 2768242097, 4294967297, 24243078582, 343698067445, 367941146027, 18740755368795
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
Write the convergents directly underneath the partial quotients (A014572) for 0.412454033... starting with the first partial quotient, 2: [2, 2, 2, 1, 4, 3, 5, 2, 1, 4, ...] such that [2] = 1/2, [2, 2] = 2/5, [ 2, 2, 2] = 5/12 and so on, the convergents being: 1/2, 2/5, 5/12, 7/17, 33/80, 106, 257, 563/1365, 1232/2987, 1795/4352, 8412/20395, ...
|
|
EXAMPLE
|
[2, 2, 2, 1, 4] = 33/80 = 0.4125.
|
|
MATHEMATICA
|
mt = 0; Do[ mt = ToString[mt] <> ToString[(10^(2^n) - 1)/9 - ToExpression[mt]], {n, 0, 7}]; d = RealDigits[ N[ ToExpression[mt], 2^7]][[1]]; a = 0; Do[ a = a + N[ d[[n]]/2^(n + 1), 100], {n, 1, 2^7}]; f[n_] := FromContinuedFraction[ ContinuedFraction[a, n]]; Table[ Denominator[f[n]], {n, 1, 28}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|