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Search: id:A085395
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| A085395 |
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Denominators of convergents to the Thue-Morse constant .41245403364... |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Write the convergents directly underneath the partial quotients (A014572)for .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...
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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[ Denominator[f[n]], {n, 1, 28}]
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CROSSREFS
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Companion numerators are A085394.
Cf. A085394, A014572, A014571.
Adjacent sequences: A085392 A085393 A085394 this_sequence A085396 A085397 A085398
Sequence in context: A041889 A055906 A002355 this_sequence A041641 A131091 A116728
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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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