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Search: id:A154742
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| A154742 |
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Denominators 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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| 1, 0, 1, 1, 2, 11, 13, 24, 85, 534, 619, 2391, 7792, 80311, 810902, 891213, 1702115, 2593328, 14668755, 31930838, 110461269, 142392107, 252853376, 900952235, 5658566786, 6559519021, 58134718954, 4308528721617, 8675192162188
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OFFSET
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-2,5
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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[ {1, 0}, Denominator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
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CROSSREFS
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Cf. A154739, A154740 and A154741 for the decimal expansion, the continued fraction and the numerators of the convergents.
Sequence in context: A022115 A042453 A041885 this_sequence A063587 A038972 A105887
Adjacent sequences: A154739 A154740 A154741 this_sequence A154743 A154744 A154745
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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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