A154750 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.

1, 0, 1, 1, 2, 3, 14, 87, 101, 289, 679, 1647, 2326, 3973, 26164, 30137, 5420687, 249381739, 254802426, 504184165, 1767354921, 4038894007, 5806248928, 9845142935, 35341677733, 221895209333, 701027305732, 922922515065, 1623949820797

Offset

-2,5

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

Crossrefs

Cf. A154747, A154748 and A154749 for the decimal expansion, the continued fraction and the numerators of the convergents.

Sequence in context: A064184 A366326 A203761 * A041167 A294380 A343261

Adjacent sequences: A154747 A154748 A154749 * A154751 A154752 A154753

Keyword

nonn,frac,easy

Author

Stuart Clary, Jan 14 2009

Status

approved