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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.
4
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
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
KEYWORD
nonn,frac,easy
AUTHOR
Stuart Clary, Jan 14 2009
STATUS
approved