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.

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

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