A154745 - OEIS

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

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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