A179823 Denominators in the approximation of sqrt(2) satisfying the recurrence: a(n)= [a(n-1)*a(n-2)+2]/[a(n-1)+a(n-2)] with a(1)=a(2)=1.

1, 1, 2, 5, 29, 408, 33461, 38613965, 3654502875938, 399133058537705128729, 4125636888562548868221559797461449, 4657508918199804645965719872781284840798220312648198320

Offset

1,3

Comments

The recurrence is a transform of the Babylonian (Newton's) method for square root computation: a(n+1)= N/2a(n)+a(n)/2 = (a(n)^2+N)/2a(n).

Links

Table of n, a(n) for n=1..12.

Example

1/1=1.0, 1/1=1.0, 3/2=1.5, 7/5=1.4, 42/29=1.41379.., 577/408=1.4142156,... - R. J. Mathar, Nov 03 2016

Mathematica

a[1] = a[2] = 1; a[n_] := (a[n - 1] a[n - 2] + 2)/(a[n - 1] + a[n - 2]); Denominator@ Array[ a, 12] (* Robert G. Wilson v, Aug 03 2010 *)

Crossrefs

Cf. A179907, A000129, A051009.

Sequence in context: A103592 A209428 A098026 * A064098 A181078 A265773

Adjacent sequences: A179820 A179821 A179822 * A179824 A179825 A179826

Keyword

nonn,frac

Author

Mark Dols, Jul 28 2010

Extensions

a(10) - a(12) from Robert G. Wilson v, Aug 03 2010

Status

approved