A154741 Numerators of the convergents of the 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, 0, 1, 1, 6, 7, 13, 46, 289, 335, 1294, 4217, 43464, 438857, 482321, 921178, 1403499, 7938673, 17280845, 59781208, 77062053, 136843261, 487591836, 3062394277, 3549986113, 31462283181, 2331758941507, 4694980166195

Offset

-2,6

Links

G. C. Greubel, Table of n, a(n) for n = -2..1000

Example

sqrt{1 - 1/sqrt{2}} = 0.541196100146196984399723205366... = [0; 1, 1, 5, 1, 1, 3, 6, 1, 3, 3, 10, 10, ...], the convergents of which are 0/1, 1/0, [0/1], 1/1, 1/2, 6/11, 7/13, 13/24, 46/85, 289/534, 335/619, 1294/2391, 4217/7792, ..., with brackets marking index 0. Those prior to index 0 are for initializing the recurrence.

Mathematica

nmax = 100; cfrac = ContinuedFraction[ Sqrt[ 1 - 1/Sqrt[2] ], nmax + 1]; Join[ {0, 1}, Numerator[ Table[ FromContinuedFraction[ Take[cfrac, j] ], {j, 1, nmax + 1} ] ] ]

Crossrefs

Cf. A154739, A154740 and A154742 for the decimal expansion, the continued fraction and the denominators of the convergents.

Sequence in context: A128850 A042025 A041072 * A041999 A041319 A042315

Adjacent sequences: A154738 A154739 A154740 * A154742 A154743 A154744

Keyword

nonn,frac,easy

Author

Stuart Clary, Jan 14 2009

Status

approved