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A085394 Numerators of convergents to Thue-Morse 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 7 10:38 EST 2021. Contains 341869 sequences. (Running on oeis4.)