The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #7 Mar 30 2018 08:13:09
%S 1,0,1,1,2,3,14,87,101,289,679,1647,2326,3973,26164,30137,5420687,
%T 249381739,254802426,504184165,1767354921,4038894007,5806248928,
%U 9845142935,35341677733,221895209333,701027305732,922922515065,1623949820797
%N Denominators 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="/A154750/b154750.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[ {1, 0}, Denominator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]
%Y Cf. A154747, A154748 and A154749 for the decimal expansion, the continued fraction and the numerators of the convergents.
%K nonn,frac,easy
%O -2,5
%A _Stuart Clary_, Jan 14 2009