A085394 Numerators of convergents to Thue-Morse constant.

0, 1, 2, 5, 7, 33, 106, 563, 1232, 1795, 8412, 18619, 27031, 153774, 6793087, 6946861, 34580531, 41527392, 117635315, 512068652, 629703967, 1141772619, 1771476586, 9999155549, 141759654272, 151758809821, 7729700145322, 116097260989651

Offset

1,3

Links

Table of n, a(n) for n=1..28.

Formula

In continued fraction form, the Thue-Morse constant .4124540336401...; is [2, 2, 2, 1, 4, 3, 5, 2, 1, 4...], with A014572(1) = 2, the first partial quotient. Underneath each term we write the convergents corresponding to the continued fraction: [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...where the latter = .412454032...

Example

[2,2,2,1,4] = 33/80 = .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[ Numerator[f[n]], {n, 1, 28}]

Crossrefs

Cf. A014571, A014572, A085395 (companion denominators).

Sequence in context: A056442 A056443 A042931 * A041875 A072188 A277056

Adjacent sequences: A085391 A085392 A085393 * A085395 A085396 A085397

Keyword

frac,nonn

Author

Gary W. Adamson, Jun 27 2003

Extensions

Edited by Robert G. Wilson v, Jul 15 2003

Status

approved