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A154745 Numerators of the convergents of the continued fraction for 2^(1/4) - 2^(-1/4), the ordinate 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. 3

%I

%S 0,1,0,1,1,7,8,31,1000,18031,55093,458775,513868,1486511,3486890,

%T 8460291,71169218,364306381,799781980,1164088361,4292047063,

%U 9748182487,14040229550,206311396187,426663021924,632974418111,1692611858146

%N Numerators of the convergents of the continued fraction for 2^(1/4) - 2^(-1/4), the ordinate 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.

%e 2^(1/4) - 2^(-1/4) = 0.348310699749006523686374494327... = [0; 2, 1, 6, 1, 3, 32, 18, 3, 8, 1, 2, 2, ...], the convergents of which are 0/1, 1/0, [0/1], 1/2, 1/3, 7/20, 8/23, 31/89, 1000/2871, 18031/51767, 55093/158172, 458775/1317143, 513868/1475315, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.

%t nmax = 100; cfrac = ContinuedFraction[ 2^(1/4) - 2^(-1/4), nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]

%Y Cf. A154743, A154744 and A154746 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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Last modified November 14 19:57 EST 2019. Contains 329128 sequences. (Running on oeis4.)