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

0,5

Links

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

Example

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

Mathematica

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

Prog

(PARI) contfrac(sqrt(sqrt(2) - 1)) \\ Michel Marcus, Dec 10 2016
(Magma) ContinuedFraction(Sqrt(Sqrt(2)-1)); // Vincenzo Librandi, Dec 10 2016

Crossrefs

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

Sequence in context: A107951 A019646 A238582 * A190282 A164833 A248938

Adjacent sequences: A154745 A154746 A154747 * A154749 A154750 A154751

Keyword

nonn,cofr,easy

Author

Stuart Clary, Jan 14 2009

Status

approved