

A154749


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.


4



0, 1, 0, 1, 1, 2, 9, 56, 65, 186, 437, 1060, 1497, 2557, 16839, 19396, 3488723, 160500654, 163989377, 324490031, 1137459470, 2599408971, 3736868441, 6336277412, 22745700677, 142810481474, 451177145099, 593987626573
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OFFSET

2,6


LINKS

G. C. Greubel, Table of n, a(n) for n = 2..1000


EXAMPLE

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.


MATHEMATICA

nmax = 100; cfrac = ContinuedFraction[ Sqrt[Sqrt[2]  1], nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]


CROSSREFS

Cf. A154747, A154748 and A154750 for the decimal expansion, the continued fraction and the denominators of the convergents.
Sequence in context: A303914 A241457 A229208 * A240562 A091108 A179405
Adjacent sequences: A154746 A154747 A154748 * A154750 A154751 A154752


KEYWORD

nonn,frac,easy


AUTHOR

Stuart Clary, Jan 14 2009


STATUS

approved



