A154748 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.

0, 1, 1, 1, 4, 6, 1, 2, 2, 2, 1, 1, 6, 1, 179, 46, 1, 1, 3, 2, 1, 1, 3, 6, 3, 1, 1, 1, 1, 2, 1, 1, 56, 1, 1, 1, 1, 66, 1, 1, 2, 17, 8, 2, 7, 12, 1, 1, 8, 1, 2, 2, 1, 1, 2, 1, 12, 1, 2, 2, 2, 2, 1, 1, 1, 8, 1, 1, 1, 1, 2, 1, 2, 5, 1, 6, 8, 1, 1, 1, 2, 7, 1, 9, 1, 2

Offset: 0

Author

Stuart Clary, Jan 14 2009

Keywords

• nonn
• cofr
• easy

Examples

			Sqrt(sqrt(2) - 1) = 0.643594252905582624735443437418... = [0; 1, 1, 1, 4, 6, 1, 2, 2, 2, 1, 1, 6, ...].
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A154747, A154749 and A154750 for the decimal expansion and the numerators and denominators of the convergents.

Programs

Magma

ContinuedFraction(Sqrt(Sqrt(2)-1)); // Vincenzo Librandi, Dec 10 2016

Mathematica

nmax = 1000; ContinuedFraction[ Sqrt[Sqrt[2] - 1], nmax + 1]

PARI

contfrac(sqrt(sqrt(2) - 1)) \\ Michel Marcus, Dec 10 2016