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Search: id:A154739
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| A154739 |
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Decimal expansion of sqrt{1 - 1/sqrt{2}}, the abscissa of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant. |
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6
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| 5, 4, 1, 1, 9, 6, 1, 0, 0, 1, 4, 6, 1, 9, 6, 9, 8, 4, 3, 9, 9, 7, 2, 3, 2, 0, 5, 3, 6, 6, 3, 8, 9, 4, 2, 0, 0, 6, 1, 0, 7, 2, 0, 6, 3, 3, 7, 8, 0, 1, 5, 4, 4, 4, 6, 8, 1, 2, 9, 7, 0, 9, 5, 6, 5, 2, 9, 8, 8, 9, 7, 3, 5, 4, 1, 0, 1, 2, 6, 6, 6, 4, 7, 7, 8, 2, 6, 1, 4, 9, 5
(list; cons; graph; listen)
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OFFSET
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0,1
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REFERENCES
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C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5
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EXAMPLE
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sqrt{1 - 1/sqrt{2}} = 0.541196100146196984399723205366..., a root of 2 x^4 - 4 x^2 + 1 = 0.
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MATHEMATICA
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nmax = 1000; First[ RealDigits[ Sqrt[ 1 - 1/Sqrt[2] ], 10, nmax] ]
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CROSSREFS
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Cf. A154743 for the ordinate and A154747 for the radius vector.
Cf. A154740, A154741 and A154742 for the continued fraction and the numerators and denominators of the convergents.
Cf. A085565 for 1.311028777, the first-quadrant arc length of the unit lemniscate.
Sequence in context: A124602 A132707 A046575 this_sequence A136564 A136042 A166044
Adjacent sequences: A154736 A154737 A154738 this_sequence A154740 A154741 A154742
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Jan 14, 2009
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EXTENSIONS
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Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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