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Denominators 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.
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%I #4 Dec 09 2016 13:37:26

%S 1,0,1,2,3,20,23,89,2871,51767,158172,1317143,1475315,4267773,

%T 10010861,24289495,204326821,1045923600,2296174021,3342097621,

%U 12322466884,27987031389,40309498273,592320007211,1224949512695

%N Denominators 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[ {1, 0}, Denominator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]

%Y Cf. A154743, A154744 and A154745 for the decimal expansion, the continued fraction and the numerators of the convergents.

%K nonn,frac,easy

%O -2,4

%A _Stuart Clary_, Jan 14 2009