-2,5

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

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.

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

Cf. A154739, A154740 and A154741 for the decimal expansion, the continued fraction and the numerators of the convergents.

Sequence in context: A042453 A041885 A247338 * A257329 A063587 A038972

Adjacent sequences: A154739 A154740 A154741 * A154743 A154744 A154745

nonn,frac,easy

Stuart Clary, Jan 14 2009

approved