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Search: id:A093053
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| A093053 |
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Continued fraction expansion of a constant x such that the n-th partial quotient equals a(n) = floor(2^n*x), with a(0)=1. |
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2
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| 1, 2, 5, 11, 23, 46, 93, 186, 372, 745, 1490, 2980, 5960, 11921, 23843, 47686, 95373, 190746, 381493, 762986, 1525973, 3051946, 6103893, 12207787, 24415575, 48831150, 97662301, 195324602, 390649204, 781298409, 1562596819, 3125193638
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Decimal expansion is given by A093054. The partial quotients of the continued fraction expansion of 2^m*x include many similar terms. For example, the continued fraction of 2*x is given by: [2;1,10,5,1,1,11,92,46,1,1,92,1,1,185,1,1,372,2980,1490,11920,5960,1,1,11921,95372,47686,1,1,95372,1,1,...].
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EXAMPLE
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x=[1;2,5,11,23,46,93,186,372,745,1490,2980,5960,11921,23843,...].
x=1.455281692832971051393034444524589699271213777825554774132070945742167...
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MAPLE
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{L=500; x=sqrt(2); for(i=1, 10, cf=vector(L, n, floor(x*2^(n-1))); cm=contfracpnqn(cf); x=cm[1, 1]/cm[2, 1])}
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CROSSREFS
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Cf. A093054.
Sequence in context: A005986 A147878 A140992 this_sequence A075712 A000100 A083005
Adjacent sequences: A093050 A093051 A093052 this_sequence A093054 A093055 A093056
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KEYWORD
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cofr,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 16 2004
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