A154745 Numerators of the convergents of the continued fraction for 2^(1/4) - 2^(-1/4), the ordinate 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, 7, 8, 31, 1000, 18031, 55093, 458775, 513868, 1486511, 3486890, 8460291, 71169218, 364306381, 799781980, 1164088361, 4292047063, 9748182487, 14040229550, 206311396187, 426663021924, 632974418111, 1692611858146

Offset

-2,6

Links

Table of n, a(n) for n=-2..24.

Example

2^(1/4) - 2^(-1/4) = 0.348310699749006523686374494327... = [0; 2, 1, 6, 1, 3, 32, 18, 3, 8, 1, 2, 2, ...], the convergents of which are 0/1, 1/0, [0/1], 1/2, 1/3, 7/20, 8/23, 31/89, 1000/2871, 18031/51767, 55093/158172, 458775/1317143, 513868/1475315, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.

Mathematica

nmax = 100; cfrac = ContinuedFraction[ 2^(1/4) - 2^(-1/4), nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]

Crossrefs

Cf. A154743, A154744 and A154746 for the decimal expansion, the continued fraction and the denominators of the convergents.

Sequence in context: A080982 A271901 A042875 * A048064 A122605 A037953

Adjacent sequences: A154742 A154743 A154744 * A154746 A154747 A154748

Keyword

nonn,frac,easy

Author

Stuart Clary, Jan 14 2009

Status

approved