A154744 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, 2, 1, 6, 1, 3, 32, 18, 3, 8, 1, 2, 2, 2, 8, 5, 2, 1, 3, 2, 1, 14, 2, 1, 2, 190, 1, 2, 9, 1, 1, 1, 2, 4, 1, 1, 2, 5, 1, 1, 1, 1, 2, 2, 3, 1, 30, 1, 1, 5, 4, 6, 1, 3, 8, 3, 4, 6, 3, 1, 1, 1, 1, 7, 1, 68, 20, 1, 3, 1, 2, 1, 1, 2, 1, 15, 2, 2, 4, 2, 1, 2, 23, 7

Offset

0,2

Links

Table of n, a(n) for n=0..83.

Example

2^{1/4} - 2^{-1/4} = 0.348310699749006523686374494327... = [0; 2, 1, 6, 1, 3, 32, 18, 3, 8, 1, 2, 2, ...].

Mathematica

nmax = 1000; ContinuedFraction[ 2^(1/4) - 2^(-1/4), nmax + 1]

Crossrefs

Cf. A154743, A154745 and A154746 for the decimal expansion and the numerators and denominators of the convergents.

Sequence in context: A249831 A304527 A321725 * A285038 A243145 A306695

Adjacent sequences: A154741 A154742 A154743 * A154745 A154746 A154747

Keyword

nonn,cofr,easy

Author

Stuart Clary, Jan 14 2009

Status

approved