

A085394


Numerators of convergents to ThueMorse constant.


4



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
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OFFSET

1,3


LINKS

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


FORMULA

In continued fraction form, the ThueMorse 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



