A154740 Continued fraction for sqrt(1 - 1/sqrt(2)), the abscissa 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, 5, 1, 1, 3, 6, 1, 3, 3, 10, 10, 1, 1, 1, 5, 2, 3, 1, 1, 3, 6, 1, 8, 74, 2, 1, 2, 4, 2, 4, 3, 5, 9, 4, 3, 1, 1, 1, 2, 1, 17, 6, 1, 2, 12, 1, 1, 1, 2, 1, 24, 1, 2, 1, 2, 9, 989, 2, 13, 1, 5, 1, 1, 1, 64, 2, 2, 1, 1, 9, 1, 3, 1, 1, 1, 2, 3, 11, 2, 3, 1

Offset

0,4

Links

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

Example

Sqrt(1 - 1/sqrt(2)) = 0.541196100146196984399723205366... = [0; 1, 1, 5, 1, 1, 3, 6, 1, 3, 3, 10, 10, ...].

Mathematica

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

Prog

(PARI) contfrac(sqrt(1 - 1/sqrt(2))) \\ Michel Marcus, Dec 09 2016
(Magma) ContinuedFraction(Sqrt(1 - 1/Sqrt(2))); // G. C. Greubel, Jan 27 2018

Crossrefs

Cf. A154739, A154741 and A154742 for the decimal expansion and the numerators and denominators of the convergents.

Sequence in context: A010129 A073050 A366426 * A179261 A154567 A260210

Adjacent sequences: A154737 A154738 A154739 * A154741 A154742 A154743

Keyword

nonn,cofr,easy

Author

Stuart Clary, Jan 14 2009

Status

approved