A085395 Denominators of convergents to the Thue-Morse constant 0.41245403364...

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

Offset

1,2

Links

Table of n, a(n) for n=1..27.

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

Companion numerators are A085394.

Cf. A085394, A014572, A014571.

Sequence in context: A041889 A055906 A002355 * A041641 A131091 A356490

Adjacent sequences: A085392 A085393 A085394 * A085396 A085397 A085398

Keyword

frac,nonn

Author

Gary W. Adamson, Jun 27 2003

Extensions

Edited by Robert G. Wilson v, Jul 15 2003

Status

approved