A154746 Denominators 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.

1, 0, 1, 2, 3, 20, 23, 89, 2871, 51767, 158172, 1317143, 1475315, 4267773, 10010861, 24289495, 204326821, 1045923600, 2296174021, 3342097621, 12322466884, 27987031389, 40309498273, 592320007211, 1224949512695

Offset

-2,4

Links

Table of n, a(n) for n=-2..22.

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

Crossrefs

Cf. A154743, A154744 and A154745 for the decimal expansion, the continued fraction and the numerators of the convergents.

Sequence in context: A279471 A042265 A041093 * A042781 A308885 A136886

Adjacent sequences: A154743 A154744 A154745 * A154747 A154748 A154749

Keyword

nonn,frac,easy

Author

Stuart Clary, Jan 14 2009

Status

approved