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

Author

Stuart Clary, Jan 14 2009

Keywords

• nonn
• cofr
• easy

Examples

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

Links

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

Crossrefs

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

Programs

Magma

ContinuedFraction(Sqrt(1 - 1/Sqrt(2))); // G. C. Greubel, Jan 27 2018

Mathematica

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

PARI

contfrac(sqrt(1 - 1/sqrt(2))) \\ Michel Marcus, Dec 09 2016