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Search: id:A154741
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| A154741 |
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Numerators of the convergents of the continued fraction for 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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+0
4
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| 0, 1, 0, 1, 1, 6, 7, 13, 46, 289, 335, 1294, 4217, 43464, 438857, 482321, 921178, 1403499, 7938673, 17280845, 59781208, 77062053, 136843261, 487591836, 3062394277, 3549986113, 31462283181, 2331758941507, 4694980166195
(list; graph; listen)
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OFFSET
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-2,6
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EXAMPLE
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sqrt{1 - 1/sqrt{2}} = 0.541196100146196984399723205366... = [0; 1, 1, 5, 1, 1, 3, 6, 1, 3, 3, 10, 10, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 1/2, 6/11, 7/13, 13/24, 46/85, 289/534, 335/619, 1294/2391, 4217/7792, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.
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MATHEMATICA
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nmax = 100; cfrac = ContinuedFraction[ Sqrt[ 1 - 1/Sqrt[2] ], nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
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CROSSREFS
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Cf. A154739, A154740 and A154742 for the decimal expansion, the continued fraction and the denominators of the convergents.
Sequence in context: A128850 A042025 A041072 this_sequence A041999 A041319 A042315
Adjacent sequences: A154738 A154739 A154740 this_sequence A154742 A154743 A154744
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Jan 14, 2009
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