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%I #7 Mar 30 2018 08:13:03
%S 0,1,0,1,1,2,9,56,65,186,437,1060,1497,2557,16839,19396,3488723,
%T 160500654,163989377,324490031,1137459470,2599408971,3736868441,
%U 6336277412,22745700677,142810481474,451177145099,593987626573
%N Numerators of the convergents of the continued fraction for sqrt(sqrt(2) - 1), the radius vector 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="/A154749/b154749.txt">Table of n, a(n) for n = -2..1000</a>
%e sqrt(sqrt(2) - 1) = 0.643594252905582624735443437418... = [0; 1, 1, 1, 4, 6, 1, 2, 2, 2, 1, 1, 6, ...], the convergents of which are 0/1, 1/0, [0/1], 1, 1/2, 2/3, 9/14, 56/87, 65/101, 186/289, 437/679, 1060/1647, 1497/2326, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.
%t nmax = 100; cfrac = ContinuedFraction[ Sqrt[Sqrt[2] - 1], nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
%Y Cf. A154747, A154748 and A154750 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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