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%I #7 Mar 29 2018 02:45:40
%S 0,1,0,1,1,6,7,13,46,289,335,1294,4217,43464,438857,482321,921178,
%T 1403499,7938673,17280845,59781208,77062053,136843261,487591836,
%U 3062394277,3549986113,31462283181,2331758941507,4694980166195
%N 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.
%H G. C. Greubel, <a href="/A154741/b154741.txt">Table of n, a(n) for n = -2..1000</a>
%e 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.
%t nmax = 100; cfrac = ContinuedFraction[ Sqrt[ 1 - 1/Sqrt[2] ], nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
%Y Cf. A154739, A154740 and A154742 for the decimal expansion, the continued fraction and the denominators of the convergents.
%K nonn,frac,easy
%O -2,6
%A _Stuart Clary_, Jan 14 2009
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