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Search: id:A085394
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| A085394 |
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Numerators of convergents to Thue-Morse constant. |
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+0
5
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| 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; listen)
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OFFSET
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1,3
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FORMULA
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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...
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EXAMPLE
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[2,2,2,1,4] = 33/80 = .4125
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A014571, A014572, A085395 (companion denominators).
Sequence in context: A056442 A056443 A042931 this_sequence A041875 A072188 A028432
Adjacent sequences: A085391 A085392 A085393 this_sequence A085395 A085396 A085397
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KEYWORD
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frac,nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 27 2003
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 15 2003
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